There is nothing that guarantees they will exist perpetually. In even a slightly moderate global crisis (man made or otherwise) LLMs and the like will probably one of the first things to go.
Only if the electric grid shuts down. At this point, I have more faith in Anthropic continuing to exist as a going concern than I do for the U.S. government.
Open weight models are here forever for anyone who has like 16gb of VRAM and a graphics card