This is not a test that can be done by a health worker or nurse or even by a doctor or specialist unless specially trainted. RT-PCR method is very complex and takes time and also it needs to be done in very clean environment. If the sample gets contaminated in the process the test results are incorrect. So it can only be done by a trained person to be accurate. If not false or wrongly negative result can be the result. No GP or even private hospital will be able to do it effectively . The equipment and chemicals needed are also expensive so go to govt testing places

Correct.. No one said that the doctor does the test. All he does is to collect the swab - from the patients nose or the back of the throat.
The rest of the RT-PCR is done in the lab.
Also note that there are many Rapid test kits coming into the market. The Chinese had the first rapid kit, but sadly about 50% false negatives. An Israeli company sources one that gives results in 8 hours, followed by a French kit that works in 2.5 hours, both of these are claimed to be accurate. Also there's is a very recent one - an improved version of the Chinese IgG/IgM test that takes only 15 mins - but it's not approved or tested by any of the other countries as yet.
(The Chinese resorted to the CT scans as they found out that the sensitivity of the CT was near 98% - against some 68% with the rapid test at that time)