There are better rifles and cheaper and easier to find ammo available these days.
Better rifles would be a matter of personal opinon. There were some very decent Mauser 98 Types chambered for the 303 British for the Latvians as well as Martinis/Winchester M95 and likely a few more commercial types.
It just depends on personal preferences. Enfield types with Lee magazines are very efficient in the field and if it weren't for their rediculous bedding system/cost to build, they would very likely have been the basis for many commercial offerings later.
As for cheaper/easier to find ammo, at the present time, I will have to agree with what you are saying.
However, there was a time when Purple and myself can still remember when the only types of ammunition you could count on finding in outlying regions, were 303 Brit, 30-06 Springfield and 30-30 Win. This went on right to the mid seventies and longer in some areas.
Other cartridges that were usually in stock were 22LR, 12gax3/4 and 410.
Things are much better now but knocking the 303Brit would be a definite mistake if you're basing your answer on capabilities. It will do everything a 7.62x51 Nato will do at similar pressures, which fall very close.
Like everything, the 303Brit is coming to the end of its useful lifespan. Not because it isn't capable but because it's fell out of favor, mainly because of the ''dreaded rims"
If I were starting out today, I wouldn't choose the 303 Brit as my go to chambered hunting rifle either. Mostly because of lack of availability with suitable hunting bullets. If there were better options than what is presently being offered, the preference might change.