I totally get the comparison and point you are trying to make - that what is considered a 'mental illness' changes over time. A century ago women were often considered to be mentally ill if they didn't conform to social expectations.
Perhaps 'being trans' is not a mental illness, just as 'being gay' is not. If an individual believes it is possible for them to change sex, perhaps they are just misinformed and ignorant, not mentally ill.
However, if we do away with the mental illness test, and the long wait, and the 'living as a woman' requirement, if we remove the barriers for the sake of compassion, and say that any trans person can get a GRC with ease - then what happens to women's safeguards? What will stop predatory and abusive men abusing the current GRC facility to enter women's spaces with impunity?
What needs to happen is that the fiction that changing gender = changing sex should be abolished.
I am not bothered about the 'identity' of any non-binary or trans person. I would be happy for anyone to be able to get a 'gender' certificate on demand, proclaiming themselves to be whatever - as long as the whole of society, and the individuals concerned, recognises that this did not change their biological sex. The sex on the birth certificate should not be changed. All relevant official documents for adults could included boxes for 'gender' (as well as sex where essential and relevant) - would that help?
But no-one can change sex. And sex matters. Especially to women.