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In London contactless payment via credit/debit/Apple/Android has automatic daily and weekly caps

https://tfl.gov.uk/fares/find-fares/capping

Depending on the frequency of travel, it can be cheaper to get season tickets though

New York's MTA does this as well. You just need to make sure it's the same card being used.

I don't think so (not a Londoner)

It was my impression that the whole thing was just about simplification in order to provide a better service.

Sydney too, for quite a while (I am sure at least 5 yrs maybe 10)

Brisbane now as well since the past ~1 year or so, much better than the old Go Card system. The only downside in most places with these systems though is that there is no easy way to pay for e.g. children, would be perfect if you could say 3x tickets on this card when you tap in + out.