You're contradicting yourself a bit here.
If the only effect a GRC has is allowing people to falsify their legal documents have their marriage or death certified under the opposite sex to the one they actually are, why is it so important that they are allowed to do so?
Why should anyone be allowed to do that, as a matter of fact?
And even if you accept that some people find their biological sex so upsetting that they must be allowed to do this, why on earth should someone who isn't medically recognised as suffering from this condition be allowed to do it? Why on earth would someone without gender dysphoria need a gender recognition certificate?
As for the rest of your post, yes it is true that nobody is checking for gender recognition certificates on toilet doors, and that in reality trans people are already using single sex spaces intended for members of the opposite sex. It's also true that people who are known to be biologically male but who claim to have a transgender identity and do not have a gender recognition certificate have already been allowed to, for example, serve their prison sentences in women's prisons despite being a clear danger to women, and compete in women's sports despite having a clear competitive advantage over female athletes.
This is wrong.
It has always been wrong.
The fact that it has been happening for years does not make it right.
The fact that it has been happening for years is also not a justification for it to continue, or become more widespread, because 20 years ago the number of trans people was so small the chances were you would never meet one in the ladies' changing rooms at M&S or in the ladies' toilets at the theatre, and even if you did, they would probably have been making a genuine effort to blend in.
But now we are all supposed to affirm people who identify as cat gender, and people like Dylan Mulvaney who appear to have a period fetish, now Laurel Hubbard is allowed to compete as a woman at the Olympics and universities are putting posters up in the toilets telling femake students not to question the presence of male students in their single sex spaces because those male students are very vulnerable and their identities matter and they have every right to be there, we need to push back on this. This is the point in time at which women need to stand up and say, "Actually, no. We don't agree with this, we weren't consulted, we didn't consent. Society needs to find a way of accommodating trans people that isn't simply women giving up their spaces and their rights without complaint. We didn't create this problem, it's not our responsibility to solve it."
Going full self ID is clearly not the way forward. Especially since it would create a presumption in law that anyone with a gender recognition certificate should be granted free and full access to opposite sex spaces (including prisons) which would have to be challenged on an individual level, rather than the other way round.