the parties will be forced to compromise
Yes. I don't think this is a bad thing. Some countries have a history of coalition governments that work very well, Germany being an example.
Proportional representation is just that - the political positions of the representatives mirrors that of the electorate. It helps to prevent extremism, and the kind of oppositional and factional bickering that you get in 2-party systems... for example the pointless impeachment of Trump, when it was obvious that even if he'd gone on a massive killing spree with a machine gun, the Republicans would still have backed him.
To further improve a multi-party system, the number of districts could have halved, and each district would get two representatives, the candidates who receive the most and second most votes, and each voter could cast two votes in an election (but could not vote for one candidate twice).
I'm not sure about how it would work best... just that in general it's a better idea than FPTP, particularly when FPTP covers such huge regions (such as winner-takes-all for an entire state at a time).