The inherent issue with this being balanced by any loss of faith is that you can just preemptively invest your faith into spreading that religion. To give an example, lets say you start nearby a civ that founds Catholicism, and you miss out on founding a religion so you decide to take theirs. But before you take their Holy City, one of your cities gets converted to Catholicism. You can now spend all of your faith buying Missionaries and spreading Catholicism like crazy. So by the time you take the Holy City of Catholicism, two civs have been investing all of their faith into one religion, which you now get the benefit of, and you lose barely any faith since you already spent most of it. You won't get an early enhancement, but you can get an early reformation and potentially even wait for the civ to enhance on their own (since they might save more faith with you buying missionaries for them).
Auto buying Missionaries when you capture the Holy City just reduces the "skill" factor of doing the above proactively. The current system removes the specific abuse case of using another civ's first GP to found, and then your first GP to enhance, but doesn't actually solve the issue of you being able to double-invest in a religion and then take it over. No system that removes faith will be able to combat that situation.
We essentially have two separate concerns regarding the system. One is OP's situation, where you lose faith you weren't going to abuse, and the other is the situation I described above.
I think the first step is confirming what issues are we trying to avoid in regards to taking over religions. Is it just the quick enhance abuse? Or is it the idea of getting a strong religion too early off of double investment? And for how long are these concerns really relevant in a game?