No, those in power very much want you to vote. Voting is a great feel-good process that gives the illusion that the people are sovereign when in reality we have practically no power and the government can do whatever the hell it wants as long as both parties agree on it. If this wasn't a democracy it would be quite clear where the power really lies, but since it is a democracy, this problem is obscured quite nicely. A thought-provoking thread from a few days about about this: https://news.ycombinator.com/item?id=5801276
Some students were probably 'sucking up'. But nearly every student?
Being able to get a substantial number of votes is a HUGELY BIG DEAL for third parties, as at some point (I can't remember the number exactly, I think it's 4%) they start getting federal funds to aid in future elections.
A viable third party, or even better, a variety of parties would provide the electoral market place more competition, potentially stop all politicians from positioning themselves in the middle, and free politicians with real views from needing to pander to party lines.
We also have a rampant issue of uninformed voting. I'd bet there are close to 50M people who just "vote with the party" and follow their biased news network rather than learning about the candidates and issues, then forming their own opinions.
It's also important to keep in mind what "two party system" really means. In the US, for example, it is not the case that every elected official belongs to one of two parties. There are both independent ("unaffiliated") office-holders (in what would be considered partisan positions) and 3rd party office-holders. The Libertarian Party, for example, usually claims approximately 600 elected officers nationwide (not all in partisan positions however) in average years.
So, net-net, while FPTP is a bad system in many ways, one should not feel that there is no value in voting for 3rd party or unaffiliated candidates in such a system. Under some circumstances they do win, and in other cases they at least affect the outcome, which - in turn - affect the public discourse - and they may impact the Overton window as well.
I can't argue that it isn't 'throwing away' your vote, in the short term, but over the very long term, there needs to be some people throwing away their vote in order to encourage more to do so such that eventually the landscape changes.
Of course they want you to vote. Only they don't vote. They just prepay all politicians so that whichever of them wins the election is already in their payroll. Units of power are not people, are cents. When did this start?