People are lazy. You can always sell your grant as you get it, they can’t make holding stock mandatory, but a lot of people (including me) just hold the stock in a really undiversified portfolio.
They can. It's easy in private companies to limit what an employee can do with their stock, and in public companies they can insert a clause in the contract to that effect just fine. Or just have very long vesting periods.
(Of course, as a would-be employee I would take these restrictions into account when deciding where to work.)
Look up eg a 'poison pill' for an example where you don't "either own or stock or you don't". (See https://en.wikipedia.org/wiki/Shareholder_rights_plan)