Youtube et al tolerate it because these influencers posts ultimately mean more eyes are fixed on the platform to watch the actual first party advertisements. Having these influencers rely on third party sponsored posts for their funding means that youtube doesn't have to pay them very much at all.
And they can eventually change terms to charge a percentage, maybe only on the biggest channels for ease of enforcement, like record labels eventually started doing with concert tickets and merch.
Surely just by contract when they get a 'record deal', and practically by hiring the accountant who does the artists books to make sure they don't try and earn without paying the masters?