Political parties change their "offerings" when they lose votes.
Analogy: When 2 large competing grocery chains start loosing business to small organic stores the big stores will start carrying organic food. The small organic store will never dominate the big stores but they can cause the big guys to change.
They are convinced that their vote is wasted by a propaganda video going around that describes the US system as a "first past the post", in which it is impossible for third parties to win. They are convinced that third party voting is harmful as it supposedly causes a spoiler effect.
As long as people are brainwashed against voting third party by these flawed memes, the problem will remain intractable.
Of far more concern are ballot access laws that make even the formation of a third party a colossal waste of time, and partisan redistricting that even makes it impossible for the second party to win. I won't even delve into ridiculously insecure electronic voting tabulators, because I'm too likely to devolve into paranoid conspiracy nonsense from there.
Eliding over all that, the spoiler effect is what forces the two major parties to make changes to their platform in your locale. If a party believes that your vote for another party caused them to lose an election, they will certainly make an effort to kiss your ass at least once in the next cycle, becoming more like the party you voted for. It is easy to argue that voting for either of the two major parties means that you don't want them to change their platform or policies.
Voting for the party in power means you are happy with the status quo. If you are not happy, and you find the second party to be more objectionable, voting for a third party that puts you between them and the party in power on the political spectrum is the correct move. If that party is scared enough by votes bleeding from them to that party, they will shift in that direction, perhaps enough that you will be happy voting for them again.
If a new non-optimal Nash equilibrium is reached, that's fine with me, because the one we have now is absolutely terrible, in my opinion. perhaps it will inspire new political strategies that do not leave huge segments of the populace effectively disenfranchised.
(I see my belief as simple mathematics)
Originally, it was the Whigs and the Democratic Republicans. In the mid-1800s, the Republicans were a new party, and Lincoln wound up being the first president from that party.
Interesting to note that the guy who freed the slaves was a Republican, while it was the Democrats who tried to maintain slavery. During the Civil Rights movement, the parties got confused about who their core constituencies were, leading to the major shift leading to the alignment we see today.
While I'm far from confident that it's happening, it's entirely possible that today's problems like ubiquitous surveillance, brutality of a militarized police force, etc., together make up enough of a sea change in public opinion that the Parties are again susceptible to getting lost. Witness flip-flop of many people in condemning GWB while failing to protest Obama's own similar actions, or vice-versa.
A few years ago I watched a TV program about Ralph Nader and it changed the way I voted.
Like most people, I had been voting for the least worst guy who I thought could win. I think that you probably do so as well. I probably did that for the first 20+ years. Now ask yourself: "How is that working out for me? Has it made a long term positive difference?"
The major parties really can't afford to cater to our interests, at least not in deed. We frankly can't pay them enough. Unless they are independently wealthy, they can't afford to run for another term if they don't satisfy the wishes of their donors [their true constituents]. Side with your voters against the guys funding your campaign(s) - no more money for you!
So since your individual vote doesn't matter, you might as well vote your conscience and not pragmatically.