It would seem that other Rishonim disagree. The Ran in Ta’anis quotes the Ra’avad as explaining that the reason there is no added prayer of neilah on fasts like 10 Teves, 17 Tamuz, etc. is because these days are set aside for mourning the tragedies that occurred on them. Neilah is only added to fasts that are set aside as days of prayer.
The Chasam Sofer proves that this view is correct from the gemara’s explanation of why we do not move these fasts to an earlier date if they fall on Shabbos – “akdumei puranisa lo makdiminan,” we do not move up a day of tragedy. These fasts are days of aveilus, not simply days of prayer or teshuvah.
Once upon a time we discussed the view of Ramban, who holds that the takanah of the ta’anis of 17 Tamuz and the other fast days included prohibitions against bathing, washing, wearing leather shoes, etc. However, that takanah was put in place only for times of tzarah. When it is not a time of tzarah, there is no obligation to fast. The choice whether or not to do so is ours as a community. Ramban concludes that we have been mekabeil as a community only not to eat and drink on these fast days, but have not been mekabeil any of the other prohibitions. (Considering events in Eretz Yisrael, could one not make the case that we are in an eis tzarah now and the original takanah should be in effect in full force? Anyone know if this issue was raised by poskim?)
What kind of strange compromise does this kabbalah amount to? Were we mekabeil the day as a fast day or not? If yes, then how can we bathe or wear leather? If not, then why can’t we eat? R’ Yitzchok Sorotzkin explains the Ramban based on these two themes, aveilus and tefilah, that characterize the chiyuv to fast. The issurim of bathing, of wearing leather, etc. are part and parcel of designating the day as a day or tragedy and mourning. This was the original takanah of fasting, which only applies when there is an eis tzarah – a time of tragedy. Our kabbalah amounts to accepting the day as as a day of teshuvah and tefilah. For this end, it is sufficient to give up eating and drinking alone.