Delaying the start would cause too many knock on problems.
If they can't check all the bikes in time, they should skip the remaining bikes and check them after the finish.
In theory that could be worse, there have been instances I recall where a tt bike that had been checked previously was ok in other races, nothing had changed, suddenly was failing the check and the rider had to swap bikes at the last minute
Because if they rode a bike they found to fail the check, theyd get DSQd from the race.
So you can imagine them doing that check post stage, finding a bike that fails a measurement, dsq'ing a rider and the team rightly saying but we could have swapped the bike had we known that prior to the start.
It's just bad organisation by the race organisers, they could have held the start for a few minutes. Or just recognised the issue was growing and dealt with it before it caused the problems, not after.