I went through informed consent to start HRT. I think the process is a little more involved than what you've put it down to.
I got in touch with my clinic asking if I needed a referral from a therapist to start HRT. They said no, and to make an appointment. I came in, got vitals taken, and had blood work done. I met with my doctor and went over my entire medical and mental health history to see if there was anything there that may be an issue. Then we went over HRT and the specifics for female to male individuals, to include: what it would most likely do, what it definitely would not do, what it could potentially do, and things that would be irreversible once they'd happened. We talked about different medication types, common dosages, and what to expect for the first few months. She gave me the form to take home to continue to read over. She made sure I knew that there were mental health professionals on staff at the clinic in case I ever wanted to talk to someone. Three weeks later once my blood work was back, I came in and got my first dose.
Does it stop people from transitioning that shouldn't? Probably not. Anybody can look around on forums like this and figure out what the "mainstream trans narrative" is. They can lie about their mental health or past addictions they might've had. But ultimately, they're only prescribing HRT to adults who they've informed of the risks involved, and who have consented to starting HRT anyway. IMO, the process I went through was very adequate for my needs. But I've known I was trans for years and had been delaying transition for several years until I had more money saved. For people that aren't sure, they might really need to talk it through with an affirming therapist.