As a fellow professional driver, you really should know that there are many reasons for speed limits, down to road conditions, schools/hospitals/old folks homes/churches/sports fields nearby, type of road, roadworks, etc, etc, etc.
You really do just need to pay more attention to the speed limits, and stay inside them.
Delivery drivers who speed to relieve pressure really are in the wrong profession, your licence is your permit to work, you need to safeguard it if you are to provide food, housing for yourself and family.
Would it be okay to drive a HGV (or any other delivery vehicle) with tyres that are just below the legal limit? No, it is a safety issue, just as speed is.