Here in Louisville back in the 1970's there was a garage called Rent A
Wrench or something like that, that would rent out space and/or tools
as needed. They provided a lift, compressed air, wrenches and any other
tools that would be used for ordinary parts replacement-type work at so
much per hour. Customers could, of course, bring their own tools if
they had them. They closed down around 1979, don't know if it was due
to lack of demand, lack of money or what, and since then there have not
been any other shops in the area that do this.
If the unavailability or high cost of insurance is the problem, one
way around this might be to just operate without it, and advertise that
fact, therefore (in theory) discouraging lawsuits since there would not
be enough money available to make it worth a lawyer's time.
The concept of a co-op machine shop open to the public is a good one
up to a point, but if I was the owner I would want to be able to verify
that the customer knew how to operate the equipment before turning them
loose with it.

Mike