Systems are in place to support transgender people in obtaining a passport or driving licence in their acquired gender, with the appropriate security procedures in place, without the need for a Gender Recognition Certificate (GRC). Passports and driving licences are often part of the evidence provided by transgender people to the Gender Recognition Panel to obtain a GRC.
I'm not sure GRCs are the problem, so much as the willingness to alter ID documents on someone's say-so - when their whole purpose is to prove that someone is who they say they are, based on testable parameters. M or F is testable: GI not so much.
(I'm not against GI/trans identity optionally being on ID as well, because it's useful information for an otherwise potentially confused official, particularly if strip searching is called for.)
In short, it's the woolly thinking I can't cope with.