Trundling through the gish gallop here because I have opened some wine and have no work tomorrow.
No-one knows what the amended Gender Recognition Act might look like, because it hasn't been drafted yet. But it seems most likely that it will involve nothing more than a change to the administrative procedures required for the issue of a Gender Recognition Certificate. It won't affect anyone other than people who are actually applying for one.
We can get a fair idea from the government's pronouncements and from the Scottish consultation documents what the proposed new GRA might look like, and how much of a shit they give about women (image is from Scotland's wholly inadequate and possibly illegal equality impact assessment).
The proposals are to remove all the requirements for evidence. Applicants will no longer have to show they have a diagnosis of gender dysphoria or that they have 'lived in' the new gender for 2 years (in practice a few official docs in the new name - passport, drivers licence, DWP, HMRC letters, payslips, household bills etc.)
The proposals don't just change an administrative procedure for those who would have applied for a GRC anyway, they expand eligibility to anyone with £140 and a biro (fee waiver for anyone on a low income). It's true you'll also have to pay a solicitor's fee to notarise the stat dec. A quick google shows the going rate for this service is £5.
I've said earlier that a GRC is neither here nor there for trans people and that's true legally, aside from a couple of very specific situations. What the self-ID proposals do - have already done before any legal changes, is change the culture around what and who women are expected to put up with in our spaces (in the widest sense).
The other thing to consider is that the GRA interacts with other legislation. It may seem like it makes no difference to allow people to self-ID to get an obsolete document, but if another law is then amended to allow further rights to people with a GRC we will be in deep shit. For example the trans equality report also recommends changing the equality act so that sex based exceptions would not apply where someone has a GRC. The current government have said they won't change the EA but governments only last a handful of years, after that all bets are off.