That's something the UK uses occasionally to solve difficult issues.
We used one for Brexit and another for Scottish independence.
It lances the boil, in a way. That is, unless there's an argument for minority protection. But SCOTUS would be directly challenging democracy if it set aside a referendum.
For us, anyway, a referendum is almost above judicial review. It's a pure expression of the will of the British people sanctioned by the crown.
If you don't have referenda, I recommend them for the issues that are never resolved in the US. Perhaps you could use them instead of the useless senate for changes to the Bill of Rights. The senate is, of course, a hopeless means of representing popular will.