This is a really common way to structure exclusivity; we did the same thing whenever customers requested it (and we couldn’t get rid of it entirely). Charge for the exclusivity explicitly.

If they wanted named exclusivity rather than general exclusivity, we would charge a somewhat smaller amount for each competitor they wanted exclusivity from. They could give up exclusivity at any time.

That was precisely how we structured our deal with Azure, back in 2014-2016 or so.