Knowing the internet lore on a similarly spelled word makes this a bit awkward.

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I mean, why not? If post secondary is necessary to get most good jobs these days why not simply roll it into the already existing public system and provide it to all? You could include trade school as well for people more inclined in that direction.

Getting into a public university in the USA is generally pretty easy. Even if you don’t meet their criteria, you can usually get in at a community college to build up enough credits to transfer.