I wouldn't say the paper-pushing is entirely meaningless. A state-endorsed document establishing that you have formally requested gender reassignment surgery shows a lot more dedication than an ad hoc assertion of gender identity.
Of course, this creates a "papers please" scenario at the point of access. I don't think this is what anybody really wants.
The paper-pushing also has meaning in a different way. It's regressive. The more bureaucratic effort someone has to put into getting their identity rubber-stamped, the more people are going to be priced out of the entitlement, so to speak. It ends up being like a poll tax.
Society is caught on the horns of a dilemma. On the one hand, we don't want transsexuals to have to carry documents and produce them on demand to justify their access to sex-segregated spaces. On the other hand, we don't want cismales to be able to gain access to sex-segregated spaces purely on the basis of ad hoc affirmations of identity.
I don't have any idea how to resolve this dilemma. It seems like most TRAs don't either.
The way I see it, Some sort of official documentation in which gender is listed on an ID/Driver's License gives a trans-gender person a response if someone challenges their access.
If we are to have segregated spaces, there has to be some means of enforcing that segregation or they aren't really segregated. This means that the owners of that space need to be able to say "Hey, I don't think you are in the right space."
If the owner can't do that or if the owner has to accept the word of the person in question in response, then the only force of enforcement is the honor system. Unfortunately, not everyone is honorable. There are those who will break the trust.
Historically, it has been an honor system, but the owner of the space had the ability to eject people believed to be violating the honor system. I think it falls under trespassing rather than any law specifically about segregated spaces.
If access is a right based on self declaration the owner of the space can no longer use their own judgment, as attempting to invoke the trespassing law would be a rights violation. So in order to have a means of enforcement, there would have to be a means of verification. (It occurs to me that this opens the door to a new grifter scam.)
An ID is a way of providing verification. I can't think of another way to allow both the definition of access as a right
and allow the removal of those who should not have access.
Another argument is that we don't need to enforce access, but that sounds more like an argument for unisex spaces to me.
I think people have pointed out that there are laws against bad behavior that would apply. But a lot of that comes down to one person's word vs. the other because, short of physical assault, the undesirable behaviors are in private areas with no physical evidence and few witnesses.
"They were peeping at me!"
"No, I wasn't!"
"Yes, you were!"
"Prove it!"
How do you resolve that? The accused could be doing wrong. Or not. The accuser could be a bigot making something up to harass. Or not.