Among modern, established democracies, proportionality of representation is pretty closely linked to public satisfaction with government, and public participation with government. Its as close to a panacea for effective democracy as you could have -- which isn't surprising, proportionality of representation is a pretty direct measure of the extent to which a government is democratic.
> It tends to lead to a fragmented government (which is usually bad).
Any government in a system with a diversity of viewpoints is either going to be minoritarian or coalition based; winner take all tends to majority-of-a-majority -- which can be minoritarian -- and, whether it is that or not, tends also to involve non-overt coalition building in structuring big-tent parties. PR systems tend to be more likely to be actually majoritarian, and tend to feature explicit -- and thus more accountable -- coalition building. It doesn't lead to "fragmented" government by any meaningful measures.
Itssometimes portrayed as leading to less stable government, because in parliamentary systems its associated with more rapid turnover of government administrations/cabinets, but by another measure, it leads to more stable government, as while there is more frequent turnover of cabinets, there is more continuity between successive governments/cabinets, and more continuity in governments/cabinets over time.
> It also privileges party over individual candidates (which can be good or bad, but those who dislike partisanship would certainly disapprove).
Certain methods of achieving proportionality (e.g., party list systems) may do so; candidate-centered election methods with rules that produce proportional results (like single transferrable vote in small multimember districts) do not. In fact, such systems would do the opposite compared to the status quo system in the US, emphasizing individual candidates over party by offering more competition, even in general elections, between individual candidates even in districts with a clear majority for a single party.
> Most (in)famously, the Weimar Republic used PR. That didn't end well.
Constitutional provisions for Presidential rule-by-decree had a lot to do with that, PR -- or even the particular form of PR used by the Weimar Republic -- well, if you want to argue that that was responsible for something, then go ahead and make that argument.