According to US financial sources, if ARM list in the US as their only listing they will need to move their headquarters to the US in order to qualify to be part of US indexes.
So, not listing in London probably guarantees an eventual move of the headquarters, and probably sooner rather than later.
It will also put ARM more firmly under US legal jurisdiction, which in turn will cause many of their non-US licensees to elevate their RISC-V contingency plans to priority one for anything not locked into Google or Apple.
In other words, it would be the start of a long, slow. death of ARM in terms of any British connection.