Who said anything about "denying their sense of identity"? You aren't denying someone's sense of identity by not chopping off healthy parts of their body.
That's something that I keep scratching my head over. I'll address it in the context of sports, because I think it's easiest to see in that case.
What is the real, valid, identity of a young transwoman? Well, she's a male bodied individual who identifies as a woman. (Language can get so difficult. Woman/girl. Male/female. I'm talking about a teenage transgirl, and we all know what that is, even if we can't agree on what to call her....I mean...I give up. You know what I mean.) So, assuming she is not actually delusional, then she is very much aware of her male body. That body is part of her identity. She may not be happy about it, but it's there, and she knows it, and lots of other people know it, too.
So, how is it denying her identity to acknowledge it? When it comes time to race, how is it denying her idenity to have her race against other male-bodied people? Can't we let Lia Thomas (or a teenage counterpart), wear a women's swimsuit while swimming in the same races as the other male-bodied swimmers? That's acknowledging her identity, not denying it.
Likewise with locker rooms. She has a specific identity and has certain characteristics that don't fit in the locker room. People say we have to treat her exactly like all the other girls. Why? She isn't like all the other girls. Her real, valid lived experience, is different from those girls, so why do we have to treat her in the same way?
So, back to your statement, people may want to have body parts chopped off, and maybe it's even a good idea to do that sometimes. I don't know. However, altering someone's physical appearance isn't affirming their identity. At most, it might make it easier for them to affirm their own internal sense of identity, but that's not the same thing.