I'm running 26 (thank you Pirelli) on my bike. A little wider at a lower PSI does offer some additional comfort. On rolling resistance, the data suggests that at similar PSI, wider tires have lower rolling resistance. If you run them at a little lower PSI for comfort, some of that advantage goes away. The reality is that most of us mere mortals won't be terribly affected by the minimal difference in rolling resistance from running a little lower PSI. I can say my 26mm tires set up tubeless running 70-75 PSI are about as comfortable as the 28mm tubed running 80 that I had on before, though the wheels are different.
In short, no, you do not need to run 23s - I wouldn't recommend it. You'd be more comfortable and just as fast on 25s or 28s, provided you lower your pressure within guidelines.