From what I've gathered so far, researchers seem to agree that this temple was built prior to the religious reforms enacted by Kings Chizkiyahu and Yoshiyahu1. On-site, the altar and other cultish/idolatrous artifacts were found buried under the mortar floor of what was the second level of the Motza site (identified with what is known scientifically as "Iron Age II 2"; the temple being from the earlier "Iron Age II 1").
This suggests that all these objects were buried on purpose, most likely by the men of one of the previously mentioned kings, who are described as putting an end to the bamot (this site is essentially a fancy bamah).
On Chizkiyahu it says:
He abolished the shrines and smashed the pillars and cut down the sacred post. He also broke into pieces the bronze serpent that Moses had made, for until that time the Israelites had been offering sacrifices to it; it was called Nehushtan. (Melachim 2:18:4)
On Yoshiyahu it says:
Then the king ordered the high priest Hilkiah, the priests of the second rank, and the guards of the threshold to bring out of the Temple of the LORD all the objects made for Baal and Asherah and all the host of heaven. He burned them outside Jerusalem in the fields of Kidron, and he removed the ashes to Bethel.
He suppressed the idolatrous priests whom the kings of Judah had appointed to make offerings at the shrines in the towns of Judah and in the environs of Jerusalem, and those who made offerings to Baal, to the sun and moon and constellations—all the host of heaven.
He brought out the [image of] Asherah from the House of the LORD to the Kidron Valley outside Jerusalem, and burned it in the Kidron Valley; he beat it to dust and scattered its dust over the burial ground of the common people.
He tore down the cubicles of the male prostitutes in the House of the LORD, at the place where the women wove coverings for Asherah.
He brought all the priests from the towns of Judah [to Jerusalem] and defiled the shrines where the priests had been making offerings—from Geba to Beer-sheba. He also demolished the shrines of the gates, which were at the entrance of the gate of Joshua, the city prefect—which were on a person’s left [as he entered] the city gate...And the king tore down the altars made by the kings of Judah on the roof by the upper chamber of Ahaz, and the altars made by Manasseh in the two courts of the House of the LORD. He removed them quickly from there and scattered their rubble in the Kidron Valley.
The king also defiled the shrines facing Jerusalem, to the south of the Mount of the Destroyer, which King Solomon of Israel had built for Ashtoreth, the abomination of the Sidonians, for Chemosh, the abomination of Moab, and for Milcom, the detestable thing of the Ammonites." (Melachim 2:23:4-13)2
Presumably, this temple was included in one of the groups of sites decimated during either one of these periods.3
Other than an explanation for why the idolatrous objects were buried, the rest of this temple also, apparently, fits well with tradition in that its architectural design is very similar to the description of the Bayit Rishon in the Tanach. Dr. David Shapira wrote a great essay on the topic.4
Another interesting fact is that all animal bones found buried near the temple are without any mumim1, which connects with what I wrote as a comment on the question, that Dr. Yitzchak Meitlis in "Excavating the Bible" wrote:
"המידע על חיי הרוח של עם ישראל בתקופת הבית הראשון אינו רב וטבעי שהתייחסות רחבה הייתה בראש ובראשונה לעבודת האלילים...אולם יש לזכור עם זאת שהפולחן הרשמי לפחות ביהודה היה עבודת ה' בירושלים ושמות מלכי יהודה וישראל כמו שמות האנשים הפשוטים מעידים על כך. נראה כי גם שמירת שבת, חודשים ומועדים הייתה מקובלת, אף כי התוכחות הקשות הקשורות בשמירתם מעידות על כך שלא תמיד נשמרו כראוי. גם ההקפדה על קבורה מחוץ לעיר וההרחקה ממתים ייחדה את תושבי הארץ הישראלים. נראה אם כן, שיסודות היהדות לחלקים הפולחניים נשמרו והיו מקובלים בשכבות הציבור היהודאי והישראלי, אך מנקודת מבטו של המקרא, העבודה הזרה והשחיתות החברתית שנלוותה לעבודת האלילים הן שחרצו את דינן של ממלכות ישראל ויהודה." (pg. 254)
Translation (mine as I only have the Hebrew version of the book): "The information on the spiritual life of the Nation of Israel from the First Temple period isn't very much and it is only natural that references would be first and foremost to the idolatry...however, we should remember that the official cultish practice, at least in Judea, was the worship of Hashem in Yerushalayim and the names of the kings of Judea and Yisrael like the names of the commoners bear witness to this. It seems that even the observance of Shabbat, months and holidays was acceptable, even though the harsh rebukes show that they weren't always observed properly. So too the strict observance on burial outside of the city and the staying away from the deceased made the Israelite citizens of the land unique. Therefore, it seems that the Jewish foundations of the cultic worship were preserved and even accepted by the different groups of the Judean and Israelite populace, but from the POV of the Bible, the idolatry and the social corruptness that came with the idol worship were what cast the judgement of the Israelite and Judean society."
On a bit of a more drashic interpretation, considering that it seems that even while worshipping idols, the Jews kept some if not most other Torah-based practices, the comparison of Am Yisrael to a cheating wife by the nevi'im makes even more sense now: Am Yisrael were two-timing, just like a cheating wife - worshipping both Hashem, according to halacha, and those other deities, according to the practices of those types of idol worship.
Note: I just heard a lecture by Shulie Mishkin, where she talked about, among other things, a Judean temple found in Khirbet Kayaafah. The archeologist who discovered it, Yosef Garfinkel, thought the city may be the Tanachic Sha'arayim, a stronghold city on the Israeli/Plishti border and that the temple was a model for Bayit Rishon! While some of the other archeologists disagree, if Garfinkel's view is correct, then perhaps that is the origin of the Motza temple: a model for Bayit Rishon (and not the other way around, that it was modeled after Bayit Rishon) that eventually became a place of idolatry.
1 Source link.
2 Also mentioned in the verses are the destruction of horses gifted to a sun deity. A small horse statue was found among the Motza temple artifacts. Just a guess on my part, but perhaps this statue was connected to that sun-worship.
(Picture from the site of the Israeli Antiquities Authority)
According to Dr. David Shapira, the temple was built with the entrance facing the east, which is the direction facing the rising sun and brings to my mind the verse in Yechezkel about sun worship: "Then He brought me into the inner court of the House of the LORD, and there, at the entrance to the Temple of the LORD, between the portico and the altar, were about twenty-five men, their backs to the Temple of the LORD and their faces to the east; they were bowing low to the sun in the east." (8:16)
3 While to us it seems like this may have been a central idolatrous site because it was so big (and who knows, may have even been mentioned in one of the books not included in Tanach but mentioned there, such as Divrei Hayamim Lemalchei Yehudah), the fact that the Tanach doesn't refer to it specifically and, at least as far as we know, doesn't single it out among the sites destroyed, shows that in the long run, it wasn't quite as significant as it may appear to us, despite its size. Perhaps no significant events took place there and it was simply just another bamah along with many others.
4 This particular aspect of the discovery is most significant with relation to the old (but still widely popular) Biblical archeology minimalist-maximalist debate. Minimalists tend to view the majority of the Tanach as a combination of exaggerations, myths (often based on other cultures) and spiced with some facts. As such, the Tanach cannot be considered a reliable source of information when trying to understand ancient Israelite culture and various archeological discoveries. Maximalists are the opposite; tending to view the Tanach as written by authoratative figures who knew what they were talking about and were writing based on solid facts (interestingly, apparently both religious and secular people can be found on either side of the debate). With regards to Motza, for a long time minimalists have held that Bayit Rishon couldn't have been built in the time of Shlomo, only later because the Bayit architecture doesn't fit with the supposed architecture of that era. This building, built around the same time as the Bayit, is strong evidence that such a building was possible already at the time of Shlomo.