The Mishna Brurah's explanation is that "we are not established as yerei shamayim [to the extent] that angels accompany us, such we would request they wait for us until we come out."
If so, it is a function of the gavra, the status of people nowadays. A lower stature means angels not always accompanying someone. However, this is different from angels triggers by a specific maaseh, action. The gemara in Shabbat 119b:
It was taught, R. Jose son of R. Judah said: Two ministering angels accompany man on the eve of the Sabbath from the synagogue to his home, one a good [angel] and one an evil [one]. And when he arrives home and finds the lamp burning, the table laid and the couch [bed] covered with a spread, the good angel exclaims, 'May it be even thus on another Sabbath [too],' and the evil angel unwillingly responds 'amen'. But if not, the evil angel exclaims, 'May it be even thus on another Sabbath [too],' and the good angel unwillingly responds, 'amen'.
discusses special angels triggered by this specific event. This does not necessarily have anything to do with one's level of holiness.
Even if we adopt the Mishnah Brurah's explanation of this minhag (not to say the bathroom request) as Rav Yosef's Karo's reason, we should realize that Rav Yosef Karo predated the creation of the piyut of Shalom Aleichem. Rav Yosef Karo lived from 1488 – 1575, while Shalom Aleichem was authored in the 17th century. So, perhaps Rav Yosef Karo would have agreed that one should not sing Shalom Aleichem.
Meanwhile, the Arizal ((15341 – July 25, 1572) was in favor of stating the bathroom angel address. (See Shaarei Teshuva on the same page as that Mishna Brura.) And this is a matter of minhag, rather than pure halacha. Or, saying a specific address when entering the bathroom seems more like halachah, while which piyutim to sing on Friday night enters the realm of minhag. Who is to say that something as organic as minhagim needs to be systematically consistent.
I sing Shalom Aleichem on Friday night, but I don't believe that the aforementioned gemara refers to actual, winged angels. Rather, the gemara clearly carries a metaphorical message, about gaining momentum in maintaining order / disorder, in preparing for Shabbos. Not only does mitzvah goreres mitzvah, but as one succeeds in making a pleasant and orderly Shabbos one week, he has the momentum to carry that same process forward to further weeks.
And singing the piyut is a way of reminding ourselves of the gemara and its message, rather than a means of speaking to (and blessing) actual angels.