> Suppose 51% of the population is in group X and 49% in group Y. Should group X be allowed to vote for more benefits and lower taxes for themselves, while balancing the budget by increasing taxes and slashing benefits for group Y?

Representative government does nothing to stop that, except insofar as representation is non-proportional, and allows Y to do that instead of X, giving tyranny of the minority instead of tyranny of the majority.

The solution you are looking for is limited (either absolutely or procedurally) government, not representative over direct democracy.