This is really an "extra" answer augmenting, since Tetsujin has the important part.
Yes, endpin spikes definitely can damage floors. The cellist's main concern is that their instrument stay in place, not the health of the floor. The acute angle formed between the endpin and the floor means that, on a slick floor, the endpin would simply slide away from the player. This is a frequent irritation to cellists, and you sometimes see them jab their endpin aggressively into a wood floor to get a good purchase.
Mind you, many things are hard on the floor of a commercial theatre (tap shoes!), and the surface often gets a thick coat of black paint; on some stages the actual wood might be quite a ways below the paint. But when cellists meet valuable floors that proprietors feel strongly about, there can be some tension. All of the "endpin stops" that Testsujin pictured protect the floors; more importantly (from the cellist's point of view) they can reduce the chance of the endpin slipping. (The ones with straps do best at this; one end of the strap goes under a chair leg.) Also, when the floor is tile, stone, etc, the cellist can't simply gouge into the floor, so these devices become more important. Lacking them, they might look for a spot where four tiles come together; in my music school there were often small divots at these joints from decades of endpins.
So what's the point of the endpin? It "fills up the space" between the cello and the floor. With a larger instrument like a double bass there's less space to "fill up"; it's already so tall that the "playing parts" are in the right place. But if there were no endpin, then the bare wood of the bottom of the instrument would rest on the floor. This would have a number of problems; it might scratch up the instrument, it might vibrate in a buzzing way, and I suppose it might have an effect on the sound, if part of the wood were muffled. Plus, depending on the size of the instrument and the player, some height is needed to put the instrument in the perfect playing position. So even historically, we see large instruments like this with endpins, like in this picture from Marin Mersenne's 1627 Harmonie Universelle:
Smaller instruments, like the viol or the "cello-sized cello" (it's complicated) were held in a variety of ways. There was a lot of variety among bass-register bowed strings in the renaissance and baroque—they came in many shapes and sizes, had varying numbers of strings (note the five pegs in the picture above), used varying tuning intervals, had frets or didn't, etc. And although most baroque cello and viol players today support the instrument with the inside of their legs (and there are many paintings showing this hold), some paintings show larger instruments resting on a foot, or a small stool or barrel:
Eventually, by the 18th century, there is talk of wooden endpins. There's a very thorough history of endpins as someone's doctoral dissertation, with a survey of these iconographic sources and mentions in treatises.
With double basses, the endpin has much less need to sharp, since the angle is usually much less acute (that is, the instrument is more upright), so there's less chance of it sliding forward.