Short-term visas have to be prepared months in advance. They're finicky and time-consuming. For a start, when visas are required for EU musicians, etc., someone will have to be employed - more likely someones - just to organise all that. That's a cost. It's also a delay. From the musician's point of view, it will make accepting work in the UK less attractive than accepting work somewhere within the EU.
And think about the hassle of getting in place all the visas necessary for a European tour. Bearing in mind that, with sterling slumping, a lot of touring companies are relying on touring outside the UK to balance the books.
For creative industries such as film , who hire freelancers on very short work contracts, there is the huge issue of the income/payment barrier. The freelancers will almost certainly not earn enough to meet the income requirement at which the current visa barriers are set. Moreover, there is currently a ceiling to the number of these visas - and it's very low.
Likewise, a lot of creative recruitment is actual at graduate level, starting with ad hoc work during study, moving on to ad hoc work, even internships, post-graduation. Not only is student immigration going to be cut back but the visa situation kicks in for that post-graduate employment route.
Initially at least, work in the creative industry isn't very well-paid and relies on this ability to check talent out, gain experience, etc., at a low-paid level. The visa situation - which has an income threshold level - knocks all this on the head.
The UK is a very small country. It simply doesn't have the population to support world-class production in the creative industry through an internal talent pool. It needs the flexibility of having a loose immigration network behind it. This allows it to punch well above weight, making it world class, and that helps to pull in talent at a high level - a world class level.
Informally, creative industries have been assured that the government is seriously looking into radically liberalising immigration post-Brexit - presumably when the impact of cutting immigration from the EU becomes apparent and the Brexit maniacs have returned to their slumbers.
However, I don't think there is anyone who actually trusts the government on this any more.