None of what you've said here answers any of the legal problems I raised. If you're just sharing what you wish the law was, ok fine, you're entitled to that opinion, but the question you asked, which I answered, was whether your proposal is legally workable. The answer remains, no it isn't, because it's not compliant with Goodwin, or with GDPR law, and to be honest you haven't convinced me it wouldn't be seen as discriminatory, even if voluntary, to require trans people to carry different ID to everyone else.
What is important is that there should be no more of this situation where ID that purports to show natal sex actually shows somebody's chosen gender instead.
Ok, but again our current legislation around allowing trans people to update their ID is founded in their right to privacy - if people are forced to carry ID where the sex marker plainly doesn't match their physical appearance, you are forcing them to out themselves as trans, and this isn't compliant with Goodwin. Again, you can wish as hard as you please, but if the law is going to be changed, this fact can't just be ignored.
And secondly, a whole data set is rendered meaningless when a particular field in the records contains different kinds of data. A database recording some (most) people's sex but other people's gender is just a mess. You can no longer get accurate statistics from it. (Eg your organisation's pay gap between men and women. Rates and types of crime, by sex. And so on.)
It doesn't render it meaningless necessarily, all statistical calculations have a margin for error, and the usual argument here is that since trans people at best guess make up less than 1% of the population the margin of error they create is very small indeed, and becomes negligible if the dataset is large enough. Data collection also isn't grounds for legislation necessary; there's lots of data about people we could collect but don't, either because it's not the primary purpose of that particular organisation (the primary purpose of a driving license, for example, is to identify who can legally drive; that we also sometimes use it for ID in other situations is secondary) or because of concerns about privacy, data protection laws, protection from harassment/discrimination on the grounds of protected characteristics etc, all of which apply to trans status as much as they do any other characteristic.