Failure of one the fundamental mechanisms of representative democratic government calls into question the legitimacy of that government, and of that system of government.
This is ammunition for the advocates of illiberal systems.
Perhaps calling into question the legitimacy of democracy is a good thing? Indeed, why is it legitimate to violate an individual's liberties through a vote of 50% + 1 of her peers?
Edit: I'll echo the peer comment that a reasonable compromise could be smaller units of government, which better represent the people. Smaller states also the limit the scope of abuse of the people within and the threat to people without.
Someone has to decide what these liberties are. You can require a greater majority than 50%, but replacing democracy by something else does not help.
Democracy is the idea that people should have a say in how their own lives are run, the exact mechanism could be many things.
https://inews.co.uk/news/brexit/brexit-vote-results-parliame...
Out of all the alternatives it gives ammo to, those advocating for more local, directly democratic governance have been receiving the lions share compared to those advocating alternative authoritarian schemes.
Inside of Europe, I'm thinking about Viktor Orbán and Vladimir Putin. Outside, I'm thinking about Xi Jinping.