We have had a multi-winner election system in Tasmania since 1896. It is called the Hare-Clark system and has its drawbacks. 1. Candidates compete mainly with members of their own party. 2. Urban areas are favoured over rural areas in the same electorate because that is where the votes are. 3. There are no bi-elections. 4. The parties are usually very evenly balanced in numbers leading to hung parliaments. 5. The balance of power is often held by extremist groups or eccentric individuals. 6. Electorates can be very large geographically making campaigning difficult and with little commonality of interest between remote areas.
Yeah, I haven’t looked at any statistics, but anecdotally it seems like I can’t support the claim that better voting methods are that much better in practical terms. Many places have systems which seem better than that of the USA, without markedly better political results.
However, in my country, where we use FPTP, we have frequently got extremist parties in power. If seats had been given proportionally, they might not have got power, or would have to operate in Big Tent coalitions.
In the last general election, 486(!) parties fielded candidates. Of course, most of them would not reach the threshold for representation in PR. But some of them will. That would almost always cause hung parliaments.
Upside is, minorities like Muslims will get better representation. They are heavily underrepresented in legislatures due to their dispersal.