And voting is legislated by individual states, that would theoretically implement their own standards though this may be intervened upon by the federal government). Heck, even standardized testing for students is done at a state level. The SATs/ACTs are privately administered. What example of a nationwide standardized test for literacy do you have?
The problem (like with voter ID laws in the US) is that it's a very slippery slope to voter suppression, and in the US we have a very creative history when it comes to voter suppression. You'd have poll workers who would present incredibly hard passages to read to voters based on a personal judgement call (read: black voters).
I (not OP) agree that dumb people voting is a problem but the alternative is to have arbitrary suppression of votes, which IMO is worse.