Yeah, the .303 was supposed to be replaced by a rimless round even before WWI (
.276 Enfield), but various wars kept getting in the way. In the end, it wouldn't be replaced until 7.62mm NATO came around.
I'm really of two minds about that. First of all, rimless ammunition is certainly more modern and preferable to rimmed ammunition, so—considering the fact that Germany adopted the Patrone 88 in 1888 and Switzerland adopted the 7.5x55mm in 1889—the .303 British was really obsolete the day it was adopted. In fairness, the US would adopt the .30-40 Krag three years later and it wasn't until 1906 that the US got its ammunition act together, but the .303 would continue to give Britain headaches in weapons development for the next 60 years.
That having been said, the .303 served Britain well for that same 60 years, and the Russians still use the 7.62x54mmR round, which is a rimmed rifle cartridge no more advanced than the .303, and there's no sign of them switching anytime soon. The PKM is arguably the best medium machine gun in the world today and it was designed around the 7.62x54mmR, so it can't be that much of a handicap.
Britain probably should've adopted a rimless rifle round prior to WWI, but—in the end—it really didn't matter very much that they didn't.
Cheers,
Logan