Fast-tracking still involves testing. In the case of the coronavirus vaccine trials, most of them anyway, they went through all the same trials stages any other vaccine would go through. It just happened at a much accelerated tempo, with weeks between trials stages instead of many months or years. Volunteers, trials teams and vaccine stocks for the next stage were already recruited and commissioned before the completion of previous stages anticipating a green light to avoid any delays. There was still time to pull the plug at any stage though, if adverse results had been detected, as did actually happen to several candidate vaccines.

The results have been an astounding success, with vaccines that are about as safe and effective as those from previous development processes. So it is possible to safely fast track these projects with enough urgency and investment.

As you say, urgency and investment are key, and neither necessarily applies (or is worth applying) to the general case of medical research (in the absence of a once-in-a-century global urgent surge in demand for a particular slice of medical research). More specifically, it seems like much of this fast-tracking is due to:

a) the manufacturers being incentivized to dedicate resources to branch prediction, essentially making the failure path more expensive. and

b) the regulator expediting the bureaucracy for a specific set of approvals (essentially jumping the line). Presumably there are other applications that were delayed to support the expedited applications, and I'll bet the expediting process hurt overall bureaucratic efficiency.

For A, I'd assume that the option was already priced in by the pharma co's and is (in the non-urgent case) not particularly cost-effective. For B, I'm all for making bureaucratic systems operate more efficiently and responsively, but I'm not convinced that most circumstances are urgent enough to sacrifice throughput to the latency gods.

Isn't that what we did with Covid vaccines?

No, they still went through the different clinical phases that drugs or vaccines go through.