If you're grabbing lots of things because they meet some definition of rare, yeah.

If you're grabbing 720p of things you actually watched, then at 4 hours at day and 1.5Mbps an entire year of recordings would be less than a terabyte. So I'd estimate this as a $1-5 per month hobby and the time/effort shouldn't be too bad either. If they reach small NAS territory then that's a useful thing to learn. They just need to limit the 4K content.