I think the main issue with this is that pronunciation changes over time, in addition to varying by area. So if we keep changing the spelling, written works will became unreadable faster.
But I would suggest that any band names that use umlauts/foreign letters should be pronounced accordingly.
Yeees I love twenty one pilots personally, but when they started using "ø" I really wanted it to be pronounced as part of the name so they could hear how ridiculous it sounds