Some of these things are new, but some have been around for years and decades. No one HAD to buy a server - co-location/bare-metal hosting has existed for years

Some of these things are new, but some have been around for years and decades. No one HAD to buy a server - co-location/bare-metal hosting has existed for years before AWS. The same for printing. Stripe perhaps made the biggest difference, mostly because this field is more tightly regulated so there is more value to a one-stop-shop solution. While they might provide "a" solution, those "API" services also don't solve provide a complete/optimal solution (You still need to understand information retrieval to make your search work well), and they sometimes create new problems (as demonstrated by the plethora of cloud consultants). For non-core activities it could be fine, but for activities the affect the product itself (E.g., search is essential for e-commerce), outsourcing all responsibility to a vendor is risky.