Yes, but you’re also paying for overhead, like equipment, taxes, software, bookkeeping, advertising, liability insurance, attorneys, retirement savings, possibly rent and, in the U.S., a not-so-small fortune for health insurance. You’ll also be working long days (weekends included) until you get established into a routine. Lots of that extra money from contract jobs gets eaten up by all that and the downtime between jobs. You’ll also need to wear multiple hats: you’ll no longer be just a designer, you’ll be a business owner and need to wear all the hats associated with that responsibility.
As for looking for new clients, well, that takes up time too — lots of it. It’a also a job for an extrovert who doesn’t feel the dread that comes with promoting oneself and getting in front of people. It’s not that an introvert can’t do it; it’s just that it can be a source of ongoing anxiety, which can take a big toll. Then there’s the financial stability of the whole thing that’s iffy. Regular paychecks no longer happen, and it can be feast or famine, which doesn’t help with the anxiety and makes planning a bit difficult.
I’m not arguing against it by any means. For the right person with the right personality, being one’s own boss is great. For many others, though, it can be draining to the point of mental and physical exhaustion.
I freelanced full-time not long after graduating from my university design program decades ago. I did it for about four years, and all of the above things I mentioned were starting to drive me nuts. Maybe if I had stuck with it, hired an employee or two and let things level out into a routine, I could have stuck with it. For me, though, it wasn’t really worth it. I finally ended up going full-time for one of the agencies I was freelancing for and have kept my own part-time, after-hours freelance thing going ever since through multiple full-time jobs.