Demos in general are pretty rare these days too, although Bethesda as a publisher did release a demo last year of The Evil Within, but that's a linear corridior game and not a sandbox game.
It's extremely rare that single player games have public betas though, instead they are just beta tested internally by the game companies themselves. Public betas are usually to test the online capabilites of a game when a lot of people are playing it, something they can't test by themselves alone.
That said, Bethesda had a few public closed betas for expansions and DLCs, but never for the main games. So don't expect it to happen to Fallout 4 either. This happened for the Bloodmoon expansion for Morrowind, Fallout: New Vegas DLCs (Steam) and the DLCs for Skyrim (360) for a very limited amount of people. The vast majority of people who applied to those betas were not accepted into it.
Agreed. Just being able to play a small crippled piece doesn't really give a good impression of what the game has to offer.
Not to mention the resources it would take to cut the game into a smaller piece and make sure that the quests in it works and so on, so they can release it for the public. They would much rather spend resources on the actual game, than a crippled piece.