Maybe it's my age talking but if a company pulled that on me here's what I'd do:

Show up on Monday without a computer. When asked, explain that they're the employer, its standard to pay for a work machine for me, and that its downright pathetic that they can't or won't.

Yes, I'd call them out. It's clearly a power move, and I'd put it right back to them. Pathetic.

I have considered that. The only reason I will bring it with me is if I need to fill out any other on-boarding paper work, but that is the limit. Maybe off-boarding as well if they don't take it well.