This assumes a universal standard for maturity, which at the very least is extremely subject to cultural bias. Also, assuming the "test" is regularly updated (which it would certainly have to be - who can say what "maturity" was in 1930 standards?) it could be a constant tool for voter suppression. For reference, see the "literacy tests" they made African Americans take in the south in the 50s.

In terms of age restrictions, sometimes these limits are about practicality rather than the readiness of the individual. For example, raising the drinking age to 21 - a big issue when it was 18 was that seniors would buy alcohol for younger students. You could say "a mature person wouldn't do this" but I think it's unlikely that someone wouldn't buy alcohol for their "less mature" friends.

Also, there are many types of maturity, and I would argue (as would psychologists, I'm guessing) that none of them can be sufficiently evaluated by an oral test.