23 mm combined with 25 mm tyre in racing I met a guy who mixed 23 and 25 mm for his front and rear tyre respectively.

Now thinking about it, I believe it's a pretty good idea since the rear wheel bear a higher proportion of the rider's weight. Wider rear tyres would support more weight with the same pressure as the front. It also helps reduce the wear and tear on the tyre itself.

So why don't bicycle (especially racing) run a slightly wider tyre in the rear, as the rear wheel mostly bear the weight of rider? It makes the ride more comfortable, and not aerodynamically terrible as the front is still 23 mm.
I would be genuinely surprised if it made any real-world difference.  Some racers commit all sorts of voodoo... err... questionable practices on the off chance it might give them an advantage. In terms of 23 vs 25 mm tires, both sizes are frequently used by pro tour teams, if one had a distinct advantage over the other you wouldn't see both sizes being used at the same events.  It terms of aerodynamics, even for sizes up to 32 mm  there doesn't seem to be much difference in   aerodynamics drag.

In terms of comfort getting the right tire pressure for your body weight will likely have a bigger effect than 2mm gain in the tire width.

Other disadvantages include complications  introduced into the assembly and supply chain for the manufacturer, which would eat into profits.