> Set it at 5% above a given base rate (fed rate, Bank of England rate, etc) and what’s the problem?

All the credit cards I've ever had do have a variable rate like you describe, though base+5% would be pretty good. I'd expect super low rate cards like that to have limited or no rewards (which can otherwise be substantial in the US).

I'm guessing part of the reason banks dont tend to go that low is that people that carry balances as opposed to paying off their bill every month are much higher credit risks.