Yes, I think it should have remained their primary sidearm throughout the whole show. I liked that it was a pulse weapon instead of a beam weapon, but that's not why I prefer it over the phase pistol. The EM-33 had no stun setting. ENT was supposed to be a bit more contemporary than other Treks, due to its relative closeness to our own timeframe, and it was also supposed to be a bit grittier. Having the crew use a sidearm that could only wound or kill, with no easy option like a stun setting, would have fit that idea perfectly.