The problem only comes when you have 1000s of pages. You'd probably have to have a planned downtime to generate them in groups if you're on shared hosting, at least on big companies that keep a watchful eye on resources being used.
I've had my account on popular shared hosts disabled for:
1) Abusing CPU and taking too much, forcing me to upgrade or get on a VPS;
2) Sending out a mailing list too quickly;
3) Using too much bandwidth at once, but not exceeding my quota.
Shared hosting can be a headache so I'm sure there'd be problems if you're aggressively started generating caches, to include different image types that would be served depending on the user's browser/speed/preference (I.e. serving a .webp instead of the rightfully compressed .jpg).