I understand why a contractor wants to remove a middleman.
But for the client company this removal is not a good move. First, finding a worker is not the only thing an agency does - it also protects the client company from IRS claims that the contractors are employees (“sits in your office, takes orders only from you”) and hence the taxes should be paid for them. Agencies also handle the payroll for the contractors (partly because of IRS thing again, partly because client pays agency in bulk).
So don’t have your hopes high.
Removing the middleman is only possible if client is small and is not interested in more contractors or payroll services. Then agency may dump the contractor onto the client laps and leave. May. Or may not - IRS concern is there even for small companies, tho I believe (IANAL) it is unlikely IRS would target smaller clients for that unless there is an audit.