We rightly consigned that idea to the dust bin, along with poll taxes, literacy tests, etc. If you want to improve the _citizenry_, a better approach would be to support civic education.
edit: s/What/Whom/
I think there is an valid question to what extent should people and views be represented. The simplest idea is that everyone is equally represented, but every voting system I've ever heard of has a minimum age, meaning that we think you can be too young to be represented.
Also, anyone who supports a non-mandatory system also supports, perhaps not knowingly or willingly, a system where the apathetic are not represented.
So, we already have a system where we think it is okay that apathetic and young individuals aren't represented, is it really that astonishing to suggest that some people think other groups should be included or that they want to change the boundaries of the already excluded groups?
In my mind, as soon as a society makes it acceptable to look at a 17 year old and say "You are too young/inexperienced/immature to vote", that society has legitimized unequal forms of representation.
Apathy-inducing speech is not that at all -- people have to make the choice to not vote; nothing is preventing them. Where there are things preventing them, we as a nation should be doing our utmost to remove those barriers. But not voting is a perfectly valid statement to make in a democracy. It can be a statement of lack of confidence in any of the candidates, or a statement of deferring to an electorate that you feel is more knowledgeable. For example, I will almost always abstain from voting for judgeships or DAs (I live in NYC); I have absolutely no means by which to judge the performance or resumes of these individuals except in very rare circumstances.
I view this and similar efforts as direct attacks on the fabric of our society, aiming to reduce the influence of underrepresented people, to the advantage of the well-represented. In that respect, it's no different from disenfranchisement (or "structural remedies", as you so euphemistically put it).
Increasing "voter apathy" is a 100% legitimate democratic tactic, even for foreign powers.
The whole point of democracy is to canvas opinion.
If you influence opinion on an industrial scale using significant sums of cash that aren't available to most citizens, that's not true democracy - that's you buying power with money.
Not in the view of U.S. campaign law.