Why is there no FPU on (most) DSP chips?
An 8086 used less than 30k transistors. The 8087, which is the FPU for the 8086, is reported to use 45k transistors.  Faster FPUs can be even larger in terms of gate count.  So the cost in silicon die area of an FPU can be significant (over 2X?).  Power and thus heat is proportional on the order of the number of transistors toggling outputs at similar rates.

For real-time DSP, there is also the issue of deterministic latency. A simple integer multiply-accumulate unit has a fixed latency.  A really simple floating point adder does not have a fixed latency (or is either not fast or not simple) due to the potential need to normalize up to twice and/or handle NaNs and denorms.