I sort of agree, however, labelling it as "eliminating red tape" isn't fully accurate. Government officials spent their holidays reading through 1000-page documents for the approval.
Additionally it may also have impacted the product a bit. At least the uk claims that the time being doses was a bit too short in the trials, and that was done because every additional week between first dose and the second would delay the approval by one week (since the trial would take that much longer).
However, my main point is that rare side effects like the blood clots are unlikely to be detected in trials even in normal times. Basically if something happens once in 100,000 doses and you have a phase III trial where 20,000 gets the dose you are unlike to see it in the trial; even during normal times. So, the main issue with the "rush" compared to normal procedures isn't approval, testing, production but the roll-out. It seems unusual that a new drugs are given to 500,000,000 persons during the first months - but given that there are 3,000,243 confirmed dead it makes sense.