Seriously. I can't imagine a business entity that needs a high-conversion landing page, but can tolerate not owning a domain for it. If my therapist's page (from their examples) was ahoyo.to/amazing-therapy, I'd probably start looking for a new one.
I agree. And for many of these use-cases a "Facebook" page for the business would be fine. I know how we all love to hate facebook here, but for many small businesses--like the guy who fixes our neon signs--the Facebook brand page works great.
You might, but I think most people would not (for example: me, I don't care one bit). Most people wouldn't even notice the domain, and most people wouldn't know what to do with this information ("the URL is ahoyo.to/amazing-therapy and not amazing-therapy.com? OK, what does that mean?").