Separate your grounds and neutrals in the sub panels. Make SURE the sub panel feeders are terminated correctly at the distribution point. Not sure what your sub panels are fed from? I assume a center pole maybe?
Your electrician probably didn't say anything because it has been that way, right or wrong. As a electrical contractor who does a lot of agricultural work, I always do things right on my work......but it is often a real struggle to get a farmer to change something that has been "working ok" for years, even if it is not right.
Most guys don't seem to want to spend much more than they have to on electric work. I understand that.
Example, often on service calls I will notice subpanels with no separate EGC, and the neutral and grounds landed on the same bar in the panel. I mention the issues with this, and what we need to do to fix it. Often, I get the response of it works, has always worked, why change it? (not fix, change, lol)
One guy even had 12 Holstein cows die while milking one night due to stray voltage.....and couldn't convince him why his silo service needed ground rods.....after the overhead service burnt up, and it burnt all the silo unloader wire up, and wire to the rotating bunk feeder up, searching for a path to ground......It found it somehow through the rebar in the concrete and the silo unloader. some guys just don't get it.
Separate your grounds and neutrals in your subs, a ground rod at the panel is not a bad thing. Make sure your main service is put together correctly also.....that will be just as important.