The UK does in fact have such a system (unlike the US). We use first-past-the-post voting, like the US, but our Prime Minister is selected by the majority in Parliament (rather than directly). Consequently, we don't have 'cohabitation', where the PM and Parliament are of different parties (which can happen in France and other Presidential systems), and it's quite rare to have minority government, where the PM relies on the support of other parties to govern.
Having said that, our system is like the US in that our parties are strictly oppositional and have no real history of collaboration. So when there is a 'hung parliament' with no majority (like in the run up to 1979, and during the second May administration from 2017-2019) then you tend to get a disintegrating administration rather than the kind of stable coalitions that are the norm in other European countries.
MMP elections, or STV with multi-member districts, result in a broader diversity of parties being elected -- not just two opposing parties.
This allows coalitions to form around shared interests, and results in 1) politics being more representative of what voters want, 2) more moderate politics avoiding wild policy swings, and 3) politics being more constructive.
It really gives a huge quality improvement of politics moving from a binary to a plural system.
Having said that, our system is like the US in that our parties are strictly oppositional and have no real history of collaboration. So when there is a 'hung parliament' with no majority (like in the run up to 1979, and during the second May administration from 2017-2019) then you tend to get a disintegrating administration rather than the kind of stable coalitions that are the norm in other European countries.