This is funny to me because many people here (west coast of Scotland) would be more likely to identify as Protestant than think of themselves as Presbyterian or even Christian, for obvious, uh, sectarian reasons.
The trend in the US must be very much because Catholicism became destigmatised in wider American society and as WASPs lost cultural hegemony.
Catholics would answer they're Catholics because Catholicism is very much its own thing when it comes to worship and the Church over time has created a Catholic religious identity. The closest to them would probably be Lutherans and Episcopalians (the Anglican Church under its more common U.S. name). Protestantism in contrast all the denominations have borrowed from one another and the differences have gotten muddled and less important, in part due to a strong disbelief in church organization centralization. I grew up a Presbyterian, and yeah, there's things in a Presbyterian worship service that other churches don't do, but they're minor and it's not like we're wholly off the reservation from standard Protestant practice.
When the Roman Catholic Church was the only game in town, so to speak, did medieval/Renaissance-era Europeans (I'm including the British isles) always see themselves as 'Catholics' or simply 'Christians'? Or has that only been the case since the Protestant Reformation?