Is it reasonable to hire people and pay them with equity?

Regardless of whether it is ethical or not, you’re going to waste a lot of time trying to get people who will actually do it. If your startup idea is super hot, you might find people who ask for more equity and less cash, but good luck finding good people who have enough discretionary time to work in your idea for equity only. I tried for a couple years and it didn’t really work. When I finally had a little money, I was able to hire good people at a significantly reduced rate when they were both freelancers and friends, usually when they were between bigger projects, and not one of them wanted equity even when offered. Even my employees didn’t want equity, mostly because they didn’t understand it.

No. If you don't have enough money to pay people, you don't have enough to start a company. That's fine! Just be realistic about it. Not everyone can or should be an entrepreneur.

I've met and mentored a lot of companies like that, and they're never able to find anyone good to build or sell the product because talented people want cash and equity.

The usual recommendation here is to value the equity of small private startups as $0. There are too many things that can go wrong, there are too many ways the founders can screw you, and there are too many ways the investors that put real hard cash get magic equity with liquidation preference that will get all the money before you.