If I can get my probably underinformed opinion here:

With an STV system you could have multiple parties or candidates that overlap with each other a lot, without risking giving away the position to a candidate you really don't want.

Like, people could vote for Clinton, Stein, Sanders, or even O'Malley, who are all pretty similar to each other position-wise, without risking letting Trump get the presidency. At the same time, the moderate Republicans wouldn't have to choose between two candidates who don't represent them; they could go for Kasich or Paul or Bush if they wanted. It would eliminate the need for a primary process and the need for two big parties.

In terms of Congressional seats, imagine if there were, say 8 parties who all have various levels of disagreements and overlap. An issue with two sides wouldn't necessarily be an issue between the two big parties. And representatives could then vote for what they believe is the right decision instead of worrying that they'll be smeared in the next primary season for not voting with their party (because there would be no need for primaries.)

I just don't see any downsides aside from the short-term pain of switching the process.