One use case is speedrunning. If you don't have space on your PC and want to record your runs.

It works easily and keeping hours and hours of video locally still requires quite some storage space

My OBS recordings (of mostly game footage) come out to between 1 and 1.5 GiB/hour for 1080p resolution. Given that simple external HDDs start at about 20€ for 500 GiB, that comes out to 6 cents of storage per hour recorded. Your power bill for the gaming PC is going to be higher than that in some places.

OK, so we’ve established that it is possible to do it another way if you want. But why get an external hard drive if you’re happy with Twitch VODs?

Twitch VODs are only retained for 14 days (or 60 days if you're subscribed to Twitch Turbo).

Yeah but are you going to want to review years-old footage or stuff from the last few weeks?

I have only streamed for slightly over a year, so I cannot say anything definite about "years-old footage". But I can absolutely see myself going back to that footage when I get nostalgic about any of the games that I've played. Especially with games that you can only realistically play once, like Outer Wilds.

I only have really used it for fighting games and my object was more to look for issues in my game. So there isn’t that much point to looking at very old footage.

I myself have used it for this purpose so I don’t think it’s a massive stretch.