You are right about the wide variability in recommendations for treating anal and especially intra-rectal warts; and I agree that in general those who are trained surgically (surgeons, proctologists) tend to be more aggressive. After all, that's how they trained: the only rectal warts patients they ever cared for were those who needed (at least in their supervisors' view) surgical treatment. Also, among the non-surgical approaches, there have never been direct comparative studies to show whether one recommended treatment works any better than the next (podophyllin, podofilox [Condylox], imiquimod [Aldara], trichloroacetic acid [TCA], cryotherapy [freezing], electrocautery, laser cautery, etc). Thus personal opinion of providers and their own past experience determines recommendations to patients.
My view and that of most STD specialists is much more like your primary MD's. Frankly, there simply are no data that aggressive treatment, especially by surgery, is better at curing warts either for the short or long term; and there is no doubt the procedures themselves are not benign and the recovery is painful and often prolonged. And I stress that such treatment probably cures nobody: getting rid of visible warts is not the same as getting rid of the virus; it is nearly impossible to visualize all warts inside the rectum, so small ones inevitably are left behind (which probably is one reason why every time you go back for TCA, more treatment is needed); and there are no data to show a lesser recurrence rate following aggressive treatment. In my STD clinic, we don't even look for internal rectal warts in people who present with anal warts.
So the direct answers are: 1) Yes your treatment is "correct", but that doesn't mean it is the only option or that it is necessarily best for you. 2) TCA has no side effects other than the direct irritation of tissues, which is why it works against warts. There is no maximum treatment. But please understand I'm not much of an expert on the stuff: I have never used it! My clinic has always stuck with podophyllin, cryotherapy with liquid nitrogen, and in recent years, prescriptions for podofilox or imiquimod.
I hope this helps a bit. Good luck-- HHH, MD