I would prefer a candidate who was the first choice of 30% of Party A voters and the second choice of 40% of Party B voters over a candidate who was the first choice of 65% of Party A voters and the second choice of 2% of Party B voters.
Admittedly, RCV doesn't guarantee this, but it seems much more promising. If you can get winners that 70% of voters can live with, that seems better than the current situation. And it would change strategies dramatically. I would expect fewer appeals to mobilize extremist bases.
I think it would also make voting more granular. People would focus on individual issues more. Their first choice might look the same as today, but for their second choice should they choose the guns-rights abortionst or the gun-control pro-lifer? That second choice now impacts the election result in a meaningful way.
It's when a Condorcet winner does not exist that Condorcet compliant methods get hard to explain.
There are alternatives to IRV, almost every single one of which is better. IRV is a bolt-on plug-n-play implementation to existing winner-take-all voting for lazy bureaucrats.
In practice, ranked-choice voting means instant runoff voting, where you basically throw out candidates who didn't get enough votes until you get someone who wins. In the US, this means that it's still going to be a choice between the Democrat and the Republican, but you'll get 10% or so of the population to feel comfortable voting for $THIRD_PARTY knowing they can still express their opinion in the Democrat-Republican race. It's political placebo, except if the results are even somewhat messy, you'll get bellyaching from people who do bad statistics to say they should have won (witness the recent Alaskan election decided in this manner).
There's another set of ranked-choice voting based on Condorcet methods, which run all two-way races simultaneously and picks the candidate who wins all of their races (with different variants for handling the case who no one can do this [1]). The downside of these methods is that they're more confusing and, if you thought that instant runoff produces unclear mandates, Condorcet methods are going to render those results even less clear.
Ultimately, the ills of American politics have very little to do with its use of the first-past-the-post voting system; switching to different systems are likely to produce the exact same results [2].
[1] The most intellectually honest, IMHO, is to just declare the race at a tie in this case. I imagine that politics would be better if we were more honest about very close results indicating ties rather than pretending that it's a decisive mandate for victory.
[2] Another statistic to remember is the vast majority of people will vote for an extremist on their side of the aisle over the moderate on the other side.