Yes, of course it has to be all universities - otherwise the mid tariff ones would slaughter the student recruitment low tariff ones (and they'd go bankrupt). And it's not just about clearing: without number caps higher tier universities could choose to confirm way down on their firms, leaving no insurances for universities that rely on these to make up their numbers.
I'm not sure what the issue is: numbers are going to be capped at around last year's levels. This means that students should have about the same chance of getting in as they did last year. Almost all offers were made by UK universities before the number caps were agreed, so were made on the basis of project certain numbers of firms, acceptances after results etc.
Actually, all UK students will probably have a better chance at getting places this year than usual because a significant fraction of students will be looking to defer and it's still a low birth rate cohort. Also UCAS have extended the deadline for student decisions until mid June so a lot of students haven't actually decided on firms yet.