There is definitely room to view Ta'anit Esther as distinct from the other fasts, for the reasons you outlined in your question.
If we consider Rambam's presentation of the fast days in Chapter 5 of Hilchot Ta'aniyot, he describes the four fast days of 3 Tishrei, 10 Tevet, 17 Tammuz and 9 Av as:
יָמִים שֶׁכָּל יִשְׂרָאֵל מִתְעַנִּים בָּהֶם מִפְּנֵי הַצָּרוֹת שֶׁאֵרְעוּ בָּהֶן כְּדֵי לְעוֹרֵר הַלְּבָבוֹת לִפְתֹּחַ דַּרְכֵי הַתְּשׁוּבָה וְיִהְיֶה זֶה זִכָּרוֹן לְמַעֲשֵׂינוּ הָרָעִים וּמַעֲשֵׂה אֲבוֹתֵינוּ שֶׁהָיָה כְּמַעֲשֵׂינוּ עַתָּה עַד שֶׁגָּרַם לָהֶם וְלָנוּ אוֹתָן הַצָּרוֹת. שֶׁבְּזִכְרוֹן דְּבָרִים אֵלּוּ נָשׁוּב לְהֵיטִיב שֶׁנֶּאֱמַר (ויקרא כו, מ) "וְהִתְוַדּוּ אֶת עֲוֹנָם וְאֶת עֲוֹן אֲבֹתָם" וְגוֹ':
[D]ays that all the people of Israel observe as fasts on account of the tragic events which occurred on them, the purpose being to appeal to the hearts and to lay open the paths of repentance. This serves as a reminder of our evil doings, and the deeds of our fathers which were like ours now, resulting in the afflictions endured by them and by us. By remembering these things we are likely to repent and do right, as it is written: "They shall confess their sins and the sins of their fathers…" (Leviticus 26:40).
(Hilchot Ta'aniyot 5:1)
In contrast, when it comes to Ta'anit Esther, he writes simply:
וְנָהֲגוּ כָּל יִשְׂרָאֵל בִּזְמַנִּים אֵלּוּ לְהִתְעַנּוֹת בְי''ג בַּאֲדָר זֵכֶר לַתַּעֲנִית שֶׁהִתְעַנּוּ בִּימֵי הָמָן שֶׁנֶּאֱמַר (אסתר ט לא) "דִּבְרֵי הַצֹּמוֹת וְזַעֲקָתָם".
All the Jewish people are accustomed nowadays to fast on the thirteenth day of Adar in remembrance of the fast observed in the days of Haman, as it is written: "Regarding their fasting and wailing" (Esther 9:31).
(Hilchot Ta'aniyot 5:5)
One could read Rambam as saying that Ta'anit Esther is merely a commemoration of the fasting that took place in the days of Haman. This is in contrast to the other four fast days, which are times of repentance for our current sins that are the cause of the ongoing consequences of historical national tragedies.
This is taken one step further by Ra'avad (quoted in Ran to Rif, end of Chapter 2 of Ta'anit) who wrote that:
י"ג אינו דומה לשאר תעניות דזכרון הוא לנס שנעשה בו ועוד שיש לנו סמך בכתוב שאמר וכאשר קיימו על נפשם דברי הצומות לומר שכשם שקבלו עליהם לעשות י"ט כך קבלו עליהם דברי הצומות וזעקתם כלומר לעשות תענית בכל שנה ושנה
The thirteenth [of Adar] is not similar to other fasts, for it is a commemoration of the miracle that occurred on that day. Also, we have a support to it from scripture which writes "As they accepted upon themselves the matter of the fasts" i.e. just as they accepted upon themselves to make a festival, they also accepted upon themselves the matter of the fasts and the crying, meaning to fast every year.
One can understand that for Ra'avad, Ta'anit Esther is not a sad day at all, but is instead an integral part of re-enacting/commemorating the entire Purim miracle.
This view of Ta'anit Esther may have halachic ramifications as well. See this article for an in-depth discussion. For one key quote:
Rav Soloveitchik, as quoted in Rav Michel Shurkin’s Harerei Kedem (188), noted a number of practical ramifications of this question. For example, would the Rambam’s ruling (Hilkhot Ta'aniyot 1:14) advocating that one refrain from "idunim" (entertainment or physical delights) on fast days apply on Ta'anit Esther? If we place Ta’anit Esther in a separate category from the other fasts, as a festive, rather than mournful, occasion, then we would likely permit such activities. Indeed, the work Piskei Teshuvot (686:2) rules that on Ta’anit Esther one may listen to music and prepare new clothing, activities which are generally discouraged on other fast days.