Yes, but (to name just a few things)
the concept of parental choice (actually, what one gets to express is a preference, not a choice) is deeply ingrained in the admissions code and in the wider politics of school admissions and many people would fight hard to keep it
the 'local schools for local children' argument is very attractive if your local school is excellent or offers something that your child wants or needs (such as wrap-around care or a languages specialism), much less so if your local school is failing or offers something you definitely don't want (eg is a faith school for parents not wanting that)
predicting the number of school places required isn't as easy as one might think, because of rapidly-shifting patterns of migration (national and international), peaks and troughs in the numbers going into private education etc
not every school has the capacity to cater for all the children for whom it is the nearest school
because the law sets a limit on infant class sizes of 30 pupils, it isn't possible - and isn't a good use of resources - to run one school with a reception class of (say) 33 pupils and another one with 37
even so, the use of distance to school as the main admissions criterion (after looked after children, special need and siblings) does give the most local children priority in getting a place