That’s a good question. In my experience: most companies want to hire full time resources most of the time. Some tasks really are not compatible with part time work, e.g. anything with site-ops responsibilities.
Find a client that wants you bad enough to forgo their preference for full time, and make sure the work you’re doing allows for it.
It helps to be more senior and have a longer proven track record.
In one case I had a 6 month contract building internal tools for a large company. It was a very unpleasant job, but they really liked me. After the 6 months were up, they offered me a FTE position. I politely said I had other goals I wanted to pursue. I had no intention of continuing with them, but they were persistent and we were able to negotiate to two days a week.
In two other cases startups approached me and I was honest and said I liked them but I didn’t have 40 hours a week to devote to their project, and they were cool with part time.
Earlier in my career I also worked freelance gigs with variable hours, little projects or on-call. That wasn’t so great, haggling with clients, more overhead (billing, unpaid travel, etc.) —- a lot less money and more headaches.
Presuming you're working with your client directly and success is in measured in outcomes not hours, you get to craft exactly the engagement that works for both parties.