It doesn't work when you don't have a defined mechanism to enforce the balance after the check. These historical documents were written when your word meant something. Like they said above it works when people are doing things in good faith.

Granting legislative powers to the executive is not a check or balance, it disrupts the separation of powers.

It is not a legislative power though. A veto is not the executive writing a law. A veto is the executive saying "hey Senate, this bill sucks and I don't want to implement it. Go back to the drawing board and either make something I like, or make something that all of you like more than 2/3." Its a forced reconsideration that can avoid hastily written laws passed on a 50+1 and create laws that are more broadly palatable to the country as a whole.

Again, it makes sense in a rational system, with rational people- something we haven't had since before Reagan.

An alternative option as well.

If the president veto's a bill passed by super majority, whatever the difference is to make the vote fail, that many people need to actively step forward to say their vote will change to oppose it.

If enough people step forward that voted for it, then a new vote happens.

Otherwise, nothing happens and no effort needs to be expended on it. The senate can just shrug it's shoulders and move on.