Stringent FDA approval process certainly slowed the testing process down, but this cannot be blamed for the spread of the virus. Other countries, such as the UK, have not set up testing centres and yet have seen the virus spread at a slower pace to the US.
Had the White House intervened and made testing a priority, it is highly likely that this process would have been relaxed some time before. Instead, President Trump lied furiously about the availability of testing - claiming that any citizen who wanted a test could get one whenever they wanted.
This was an outright lie: Lawrence Gostin, a public health expert at Georgetown University responded to this claim,“The president says anybody who wants to be tested can be tested, but that’s self-evidently not true"
The FDA could have moved at a faster rate. But ultimately, it was following instructions from above.