Usually we just vote, they find a coalition and it stays that way for a few years
About coalitions: they mean that the parties in power need at least 50%, so if there's not a single party with over 50% ("absolute majority") they need a partner. The big parties in my country usually get 20-30%.
I've read that in Belgium (the worst offendor in this regard), the regional governments have so much power that not having a national government for a year or so isn't much of a problem.
Belgium is a federal country, like Germany or the US. The regions have control over some things, not everything.
Plus the current federal government stays as caretaker until a new government is formed.
I'd argue that political stability consists of and depends on at least rule of law, separation of powers and democratic representation. The EU and its member still have a lot to progress in this regard, though. Coalition building is kind of a comprise towards building pluralistic quasi-consensus based decision-making.
IMO, coalition political systems have the potential to politically deal better with long-term issues as small parties can influence governments beyond a single term. Green parties, but unfortunately also far-right parties, for example can thus push for their topics.
The US also had a coalition, the National Unity Party during its Civil War.