Say it is true that "orgasms originate in the brain". That leaves open the stimulus or catalyst, since these orgasms are not spontaneous. Perhaps one sees something sexy and experiences an orgasm. Or one has wicked thoughts and experiences an orgasm. The idea/argument here is that one such input is the stimulation of sensitive erogenous zones. Therefore, removal of one such region intentionally and avoidably limits the range of experiences or inputs.
So, while it may be possible to have orgasms without penile stimulation, that does not negate the claim that penile stimulation leads to orgasm. And if penile stimulation reduces to the stimulation of nerve endings or some such, and if their number and sensitivity matter, then their removal reduces penile stimulation an hence one avenue to orgasms.
What remains is the question: "so what? There are other avenues". Which does not address the puzzle of why one would limit one's avenues. One answer could be that we do so to gain other benefits (reduced risk of infection through "unsafe" sex) -- this line of reasoning is quite different (as I described earlier).
I am not very puzzled by the idea that stimulation of the penis (among other things) has something to do with orgasms. Whether this stimulation varies as a function of the number of nerve endings, and so on, is beyond me -- though its not clear that the objection to the amputation is based on nerve ending count -- but something I assume is accepted (or some variant of it is accepted) since the idea was not challenged.
In the analogy you offered, you mention "severe burns" to your hand: would you equate "severe burns" to "damage"? Many, I think would. And I also think that: (a) most would prefer not to inflict burns on themselves, even under anaesthesia, and (b) have the condition reversed if possible. Again, there may be other considerations: perhaps the hand was intentionally burnt to avoid more severe "damage", etc. And again, that's a different line of reasoning.
With apologies for building on your hand-burn example,
--ravi