I think that mandatory voting will just cause people to randomly click on witnesses until they have enough to unlock whatever feature they want to use, which i don't think helps anything, and might even make things worse as @ura-soul pointed out.
I think it's ok, if not better, for people who don't care to not vote. The issue isn't how many people vote, it's how many people care about voting and care who is running the government/platform/whatever that they are a part of.
I like to tackle problems piece by piece instead of making large changes all at once. I think the first and primary problem regarding people voting and caring about witnesses right now is awareness - most people have no idea what witnesses are or that they can even vote for anything.
So I think a good first step is to increase awareness and see how that goes before moving to more drastic measures.
I agree with @yabapmatt that without an increase in understanding of what witnesses do and how to choose one you support, the outcome may not be what an optimist might expect. Just having promo boxes on steemit to prompt people to go read an intelligently (and fairly) written informational page about witnessing with links for users to learn more and learn about the witnesses themselves - would be a great start.
Unfortunately, we can come up with nice ideas all day long but from what I am seeing Steemit Inc. are not particularly focused on delivering them anyway currently.
My suggestion is to maybe start up a profile/movement along the lines of @promo-steem that promotes witnessing to raise awareness. This would not rely on Steemit Inc. agreeing to anything or having to dedicate any resources. Witnesses could come together to upvote posts that promote witnessing in general and the posts would have to be neutral to ensure no one witness gets an unfair advantage.