Of course a random person can't just set up a law firm, just as a random person can't start up as an independent financial advisor, or surveyor, or architect, or auditor or liquidator.
There are minimum professional qualification requirements, practising certificiates, professional indemnity insurance, money laundering registrations, etc etc etc.
But someone who's qualified in a profession and has the requisite working experience, can pretty easily do all the box-ticking, get the certificates, insurance, etc that they need. They'll know what needs doing as they'll have been doing it in the workplace.
It's what I did, as a chartered accountant and registered auditor. Just ensured I got the practising certificate and relevant experience whilst working for others and then took the plunge to do it on my own. Insurance and regulations wasn't too onerous.
I've a couple of self employed solicitors with similar background who've done the same. And 3 independent financial advisors - worked for others first, got the professional qualifications, got the experience signed off and then go on their own.
We're talking professionals here - none of the setting up on your own is rocket science.