In the US, I think a big factor was world events getting so much faster while Congress did not. For an extreme example, the President has the authority to unilaterally launch a massive nuclear strike, because there wouldn’t be time to get Congress together in a crisis.

It also seems to be a way for Congress to dodge responsibility. If you pass legislation to fix something by giving the president powers, you can claim credit. If it goes wrong, you can blame the president.