It's a good idea - in theory. But the reality is that PSL agreements are frankly a nonsense.
They exist for one sole purpose - as a mechanism to drive down recruitment fees. There is not one PSL which is so water-tight than an agency cannot get on to it, through it, or past it. The real power in determining whether a company works with a recruiter these days is not in the hands of the hiring managers (who can judge whether the recruiter knows his/her stuff) but with procurement - it's a vendor issue these days. And much of that, at least with the biggest firms, has become little more than RPO with bells on.
A good recruiter who does not have an existing mandate with x firm should tell you this, but may then suggest - of they have the networks - they can make an over the PSL introduction directly to the hiring manager who can quantify your worth to that company. Sometimes this will work sometimes not.
Also worth considering is that no firm in my experience, no matter how rigid their PSL (which once implemented becomes the doted on soilt brat of HR) the hiring managers themselves neither care about its existence, nor would they allow the PSL to prevent them making a hire they want. If you are a star restructurning guru and your CV is in the inbox of the right partner at x firm for example, the Partner will want to talk to you, and either insist the introducing firm is appointed to the PSL, or tell HR what to do with it. Cue internal wrangling which can only have one end - seniority wins - and the PSL is busted. Once the exception is made, the PSL loses credibility and before you know 5 hand picked recruitment partners become 30 or more coming out of the woodwork. Go help you if an RPO ever gets involved. At least one major consulting firm has been largely populated with utter dross through RPO, the Partners resent it and will circumvent it where they can, but the procurement issues shout louder - cost cost cost.
If you want this reality to shape your career, insist on PSLs for every role you apply for.
