Is it ok to run this car with no thermostat?
Agree, no. The cars computer will throw all kinds of check engine lights and codes. It will reduce your fuel economy and cause your engine to wear more. Whoever told you to do this is living on 50 year old bad information.
Agreed. Thermostat is a vital part of the cooling system, which is vital to efficient operation and engine life. If running with no thermostat makes things seem to be better, it is not dealing with an underlying problem.
Running a modern car without a thermostat is the automotive equivalent of touching-up X-rays so that a tumor isn’t obvious. Both practices will ultimately be fatal, but in the case of the engine without a thermostat, at least one can buy another car after this type of cover-up results in major damage.