For the record, I don't think that we're wrong to implement a minimum voting age, and I don't think toddlers should vote, but I still think it's a worthwhile thing to consider.
If (as I assume) our goal is to restrict voting to those deemed mature and of sound mind, then I'd expect to see similar laws enforcing such restrictions in other sectors of the populace. But we don't see that! Instead we see laws explicitly granting the right to vote to the elderly and mentally disabled. It's possible to end up in a situation where an individual is deemed mentally unfit to manage their own finances or medical decisions, but still able to influence the governance of an entire nation.
I'm personally quite fascinated by this. Maybe my assumptions are wrong! Wouldn't that be neat? My goal is not to suggest that our policy is bad or wrong, it's to suggest that the "allegedly unethical scenario of having a voting age" is actually quite complex and interesting!
Dumb example: Should Brittney Spears have the right to vote?
The reason is loki's fallacy is a fallacy for a reason.
For legal purposes we simply have to pick a line.
But regardless if the exact location of that line is arbitrary, it is still useful none the less.
There is no real issue with having an arbitrary line, if it is impractical to not have an arbitrary line, and useful none the less.
To give more obvious examples, we can take the drinking age, or the age of consent. Those line are arbitrary, but are still useful none the less.