Absolutely not! The choice of fixed- vs floating-point for a controller should be based on domain knowledge of the problem, and the right choice may vary depending by operation. For example your PID's integrator needs to accumulate a running sum. Fixed-point addition is well-behaved for addition, with only the need to deal with overflow (which can be dealt with; the integrator likely needs to saturate anyway to respect a physical limit, so you choose a datatype that doesn't overflow before then). Floating point addition has much more nuance; adding a small value to a large one can result in no change at all to the output, causing a controller's small-signal transfer function to change based on the system state. This can lead to all sorts of unexpected bad behaviour, like vibration and limit cycles, which might happen only in edge cases after the controller has been running for some time, and so are very hard to catch in testing.

There are also many cases where floating point is the clear winner, but again, you should think about it and not just choose floating point reflexively because it seems easier. Its convenience makes it very easy to sweep errors under a rug, and they always come back to haunt you later.