Certainly, there's merit in reducing the "gatekeeping" role of GPs. Yes, lots of patients are capable of "self referral" to the appropriate service.
For example, it took six months and several GP appointments for my son to get the magic referral for proper treatment of his ingrown toe nail. Once referred, he was seen for review within a week and then had the sides of his toenail removed the week after. That was after the GP faffing and farting around, saying there was a massive waiting list for the podiatry dept, trying all kinds of creams, bathes, etc., and then treating the inevitable infections with antibiotics. I've had ingrown toenails myself, I knew the nail either needed removal or the sides cutting, as I'd also gone through months of my GP (twice) trying creams etc. The podiatry dept had no backlog at all - it would have been less harmful/painful and taken up less NHS resources for me to have been able to make an appointment directly with the podiatry dept. In fact, he now has an "open" appointment and can make direct access to podiatry if it ever happens again!
Likewise getting my hearing aids. What a pallaver. Took about a year of GP appointments to get the magic referral to audiology. First appointment showed some ear wax, so told to try to OTT ear wax removal drops. Went back a few weeks later to see GP - ear wax still there, so he prescribed some drops. Went back a few weeks later, wax gone, but now there was an infection, so antibiotics. Went back a few weeks later, finally, all clear, so he'd do the referral but "expect to wait a few months). After 3 months, I'd heard nothing, so phoned audiology to chase and see if they had any cancellations - they had no record of me at all, so I'd have been waiting forever had I not chased it. I phoned GP surgery, they checked records, and found referral hadn't been sent. But they can't send it now, as it's too long since my ear inspection, so I need another GP appointment to check my ears again to check no infection, no wax. Luckily there wasn't, so referral made. This time, I phoned audiology a couple of weeks later to check they'd received it - they had, and they made me an appointment about 10 days later! Finally.
In both cases, it was the GP that caused the delay, and once the referral had been made, the actual consultant with the dept and treatment was remarkably quick.
Literally all of the appointments for the toenail and ears could have been done by a nurse rather than a GP. Even better would have been the availability to "self refer", just like patients do with other NHS services such as dentistry, opticians, etc. The "gatekeeping" model is outdated for the basics.