It largely depends on the kind of bike you’re riding, what kind of terrain you’re riding on, and your goals. And, like I said, there are limits to how wide you can go before you start to see drops in performance, Same applies to going more narrow though.
To your point, yes, there is a difference between a 38 and a 45. But the loss in energy depends largely on the tire. I’ve noticed that I don’t really lose all that much energy on my 650bx47mm compared to my 700cx38mm wheelset. Why? Tire choice I think. The WTB Horizon’s I ride on don’t have heavy tread on them and thinner sidewalls, making them more supple and thus don’t lose the same amount of energy compared to a similar 47c tire with more tread.
Now, what about a 700cx47mm or higher? Would you lose more energy with a tire that big? Probably. But it’s not necessarily because the tire is wider. The real culprit has more to do with the added circumference of the tire. HUGE difference between a 38 and a 47 on a 700c rim. I honestly wouldn’t go above a 38. Any bigger and you have to work your ass off on steep climbs in lower gears.
But, again, depends on your goals. For a commuter, I would likely stick with something close to a 38 like I ride now. Really like the Rene Herse tires. Just comfy, grippy, with low rolling resistance. Noice! I like the added “free suspension” they give me compared to the 32’s I was running before. And they’re plenty fast too.