Edit: To clarify:
Is it even possible, financially speaking, to keep adding storage? I mean, advertisements don’t even make a lot of money, is the indefinite growth of server storage even sustainable?
Or will they do what Twitch does with old content and just delete them?
If you’re asking if YouTube has a finite amount of storage, the answer is yes. Assuming no safeguards were in place, you could theoretically fill up all their storage.
If you’re asking whether they will run out of storage… probably not while it is considered important. YouTube can buy additional storage space (the good ending), or they can delete content they deem unimportant (the bad ending). Or, they could decide that YouTube is “finished” and elect not to increase its storage. It’s their storage, so they call the shots.
Really, everything hosted “in the cloud” is hosted locally on someone else’s storage. If that storage dies, the data dies, unless you or someone else has a backup.
Edit: fixed for clarity