Not necessarily. Elections are run by the states, which makes changing FPTP a lot more manageable than changing, say, House apportionment (which would take a federal law), abolishing the Senate (Constitutional Amendment), eliminating the electoral college (Constitutional Amendment) or most other things people suggest to "fix" our elections.
It being a state thing means that you only need to get state legislatures (or in states with ballot initiatives enough voters) on board which is easier than moving Congress and that you can do it piecemeal - you can change individual states at a time and then use the success of the policy in the first states to promote the idea in other states. State laws are easier for the people to actually have an impact on.
I'd love to see states switch over to approval voting - it solves most of the problems with FPTP and it's dead simple to explain. Instead of picking your top pick, pick everyone you'd approve of. Whoever gets the most votes wins. No multiple rounds, or your vote counting for a different candidate depending on previous rounds or anything else. The only ballot change is "Choose every candidate you support" in place of "Choose one candidate", stubborn voters who don't want to understand a new system can just do exactly what they've always done without issue and most voting systems currently out there already effectively support it.
The people who pass laws are elected representatives.
The current electoral system works well for the current elected representatives (kinda by definition, because it's what got them elected).
So, the laws won't get changed because the people who have the power to pass the new law aren't going to pass a law that disadvantages them.
Case in point, the Liberal Party of Canada promised that if elected they'd reform the electoral system and get rid of first past the post. But, of course, FPTP is a massive advantage for the two main parties, the Liberals and the Conservatives. So, when they won the election, they quickly backed out of that promise. The only parties still promising to get rid of FPTP are the smaller parties who would have a big advantage if FPTP went away -- but, of course, these small parties can't win elections because of FPTP, so their promises to get rid of it are empty because they will never be in a position to make that change.