Ideally, the upper house is gradually stripped of its powers, as it's undemocratic by design.

IIRC it's actually somewhat rare to have a bicameral legislature where both houses have roughly symmetrical powers.

"Undemocratic by design" applies to the whole Constitution, since everything in it requires supermajorities to change. A legislature is undemocratic in that it restricts voting to representatives. Due process is another constraint on democracy. This is to say that "undemocratic" is not necessarily a bug, since pure democracy is rule by the whim of the mob.