Discopants
FTM
if your speakers are full range, definitely not necessary to have a sub.
The idea that a sub can give enough bass to speakers like P3esr is a myth. Bass freq are from about 40hz to 150hz. a sub crossed to the p3esr at 80hz will help but wont change the limitations of the small speakers in the 80 to 150hz.
What are the 80 to 150hz limitations ?
I can only imagine them to be related to being able to annoy your neighbours. My system can play up to 100dB spl but if I push it beyond 80 my wife complains.