I think it should be noted that there are varying degrees of bodily dysphoria in transgender individuals. Some feel no dysphoria, some feel little, and some feel much. Dysphoria is very real, very widely researched and provable, and is the only possible contender to be classified as a mental illness. However, assessing anecdotes from many trans people, there is often the thread of societal expectations that runs through their description of the dysphoria - the dysphoria that causes what many are referring to as "mutilation" and such to take place. In the end, it is very possible that what is causing harm to these peoples' bodies is the fact that humans are very categorical creatures and do not like to be told that they don't have enough information to categorize something. In essence, I can understand what you rigid thinkers in here are logically placing in front of you, but you very well might be contributing to mass mutilations and deception - because you cannot force yourself to accept these people as they come. They know you won't call them a man because you see a fair face and breasts - that's what's causing the dysphoria and what is leading to the mutilation and adherence to societal standards in the first place. Your argument stems from the disbelief in the existence of gender identity, and though much evidence leads to it possibly existing, you would rather be heartless and categorize "not knowing and being compassionate with respect to that absence of evidence" as "lying and being dishonest because I know that the absence of evidence is actually the evidence of absense"
I admit myself in doubting the actual existence of gender identity (which is basically gender not inherently tied to sex that can be applied to all people). That doesn't mean I should be rigid, dishonest, and utterly non-compassionate nor empathetic (which I'd describe as "evil" by the way) in positing that I am the just one in going against your preferences and disrespecting you in presence of the possibility that your condition might actually be completely non-delusional, and thus completely non-"curable". It is entirely non-scientific and dogmatic. I don't know if gender identity exists, I personally doubt it in the lack of any sort of gender I feel for myself, but that is just one mere account.
To address the thread's main question: Yes, they should, and parameters revolving around gender/sex should be more situational and descriptive. Sure, some things will become convoluted and generally non-functional, i.e. gender identification via I.D. In the desirable far future, trans people won't have to "mutilate" themselves because society will accept them without such procedures. Dysphoria, I think we'll find with inevitable progress, was a completely societally induced dissatisfaction. We have to, however, realize that progress always comes with drawbacks. Yes, you could not actively ID people by sex or gender now, because someone who has XX chromosomes, the corresponding hormones, and the corresponding body parts could be identified as male. A con indeed, somewhat countered by the fact that humans are largely linguistic and could describe someone perfectly well not using such terminology. On the other hand, there would be no miscommunications, no deception (purposeful or not), and no ambiguity as to what they're packing in their pants. But we can't have that, because enforcing a possibly inaccurate binary categorization system that you "know" is true due to a lack of evidence disproving your claim is entirely encompassing what is known as "telling the truth" and "being honest." It is more important than the mental and physical well-being of many people.
Ultimately, this is an issue of not wanting any new information to affect new, fitting changes in society. It is an issue of rigid, black-and-white thinking in a world covered in shades of gray. It is a refusal to ditch long held standards for fear of the unknown - and possibly the truth. It is a fear of having to relearn - having to critically access yourself and your own beliefs. It's a fear to move forward personally or contribute to a society moving forward collectively. It is conservatism at it's best. It is conservatism at its worst.