The problem that Mr Washington anticipates is in fact already with us, as I know from personal experience. Family members of my Colombian son-in-law abandoned attempts to visit him in Britain for a weekend when visas were demanded, but they were able to visit relations in Spain and Germany without problem. (Entry to EU permitted for 6 months before visa required.)
To return to this forum's subject - a couple of years ago I saw a Kenny Garrett group in Manchester which was minus a pianist. He had been refused a visa. After his solos Kenny somewhat awkwardly put down his horn and crossed to the piano to take reasonably good Tynerish solos.