How long are the contracts you're finding? And are you doing multiple at once? In the UK I struggle to see any contracting less than full time and six months. At which point, without annual leave, it feels like a much worse deal than an 0.8 FTE remote job.
My current one is in its 5th year.
I often do a few years on then take a year off.
Look for "initial 6 month" type listings that renew. Many business don't want full time staff, they want a workforce they can flex and will pay more for the privilege.
Recruiters typically charge approximately 10% in the markets I am familiar with.
They also act as a free sales force and have supplier agreements with end clients. These are very hard to secure directly for one man bands.
I would argue that it's not really consulting or running your own business if you are working through a recruiter. It's more akin to short term employment. That may be fine for your aims however.
But I gather many clients have a strong working relationship with one recruitment firm so that if anything goes wrong, that firm will want to maintain the relationship and find a replacement ASAP from their pool.
Most recruiters are absolute snakes. They can be very useful and you don't have to let them negotiate for you.
At the end of the day, as long as they get their cut they don't much care.
Saves me endless hours at $X/hr searching myself. It's more cost effective for me to bill a client for those hours than market myself.
If you know the industry and find good recruiters they'll break their back to place you.