Well for me it was the opposite, I had a lot of services attached to the same card and when I got a new card it was such a nice feeling that I did not have to go through the trouble of updating each of them with new card information.
PayPal and Apple's Store show me a list of all services that are authorized to pull money from my account.
CCs don't. You may have to do a nontrivial amount of research (or at least worrying) to ensure that everything is accounted for by the next charge cycle if you were to switch CC numbers without charge forwarding.
If CCs did have a paradigm of services authorized to re-bill you, then we wouldn't have people changing CC numbers to "reset" their re-bills nor to avoid future pulls from their account. But since CCs offer a UX clusterfuck, people will often find the need to clean the slate.
When I got a new card they "helpfully" sent the new number to Redbox, who then charged me a late fee when the thieves who originally skimmed my card didn't return the movie they "rented".
