An important thing to consider here- WHICH monarchy?? Absolutist old-Russia style? That's what we do have now (in all but name), with Putin being "de facto tsar". Swedish-style constitutional monarchy? Even i, who don't cherish monarchy too much generally, would agree. And so on....
Personally I favor the monarch having a fair amount of actual power to check the Parliament, but mechanisms existing for rendering them powerless for periods if they step over the line. But it would be hard enacting that in practice.