If primes derived from pi are not suspect, then that surely goes for primes derived from 1/pi, e, sqrt(2)... as well?
If someone uses 1/pi, the first question they face is going to be "why not pi". If you need a series of values, sqrt(p) is reasonable, but if you're just looking for one value then using sqrt(17) is going to look suspicious.
What about bit order, byte order?
What about them? Primes don't have bit or byte orderings. They're just integers.
If you say "I generated this prime by taking Pi, writing it as a series of bytes, permuting those bytes, and then interpreting those as an integer", people will be very suspicious.