There is no requirement at all that all fans run at the same speed. They should all be temperature-controlled & ramp up as necessary [though this is not true for all PCs, all fans.]
If you have a fully-controllable system, it may be beneficial to lift the case fan speeds & leave such as the CPU & GPU etc on automatic.
As an example, this is my machine currently idling…
Boosters 1 & 2 are for a dual CPU & do tend to always remain similar, the others I have set minimum speeds of about 1000rpm, which keeps the CPU's automatic fan speed slightly lower overall. This is the quietest way for this particular machine.
Under different loads, they will ramp up, each to a speed decided by the temperature sensors & onboard controller. Though on this particular machine I can artificially force any fan to any speed, normally I leave it under fully-automatic control, just with those minimums I specified. If I know the machine is about to be subjected to extreme loading, I will manually set the fans on high (though this does make it sound more like a hovercraft;), then back to automatic afterwards.
and once the workload reduces again to idling, they gradually all drop back to nominal.
There is wisdom in keeping input and output fans roughly balanced, so they are both doing the same amount of work, one pulling air in, one pushing it out, rather than fighting each other - though this might require some trial & error if you don't have the same number of identical fans on each end of the machine.
Overall, you can never have too much airflow - in reality it's a balance between cooling & noise.
As regards the comment that case fans are weak - mine is perfectly capable of holding up a paper tissue when the fans are running hard. It even pulled it in from 3 or 4 inches away & didn't need to cover the entire inlet to keep it there.