Anything can also be run on a cheap computer.
The difference is in speed. A cheap computer may run a big model up to a few orders of magnitude slower than datacenter hardware, depending on whether the LLM is small enough to fit in GPU memory, or it is small enough to fit in CPU memory or it is so big that it must spill on SSDs.
Depending on the application, the tradeoff between run time and run cost may happen to favor using local hardware, despite a much slower speed.
There are plenty of applications where doing them for negligible cost during an overnight job can be preferable to obtaining faster results at a very high price, for instance scanning for bugs in a mature code base using a great number of different open-weights LLMs, which can achieve similar bug coverage like using a single, but overpriced and unavailable SOTA LLM, e.g. Mythos.