How Much Engineering is Still Done by Hand These Days?

The best ones do, because all the steps you mention - CAD, simulation - are useful only when a clear concept has already arisen. The best engineers, in other words, are those who do preliminary design.

But the newbies will most always try to prove that wrong by tying to make one us look like set in our way inefficient old and outdated fogies.....

if you haven't experienced it don't think it doesn't happen.... especially in software and hardware design groups

Ignorance is...unavoidable. But results count. I see this in aeronautics, where everybody sits on his hands while the Select Few enter massive amounts of data into a computer, only to get back either nonsense or things they already know. They skipped the key step of defining a concept.

Redfred is correct, sketches & initial calcs before you do anything on screen. You need a reasonable idea of what you are modelling before you start.

Hand calcs get you that zero-th order solution to ensure that AI tool didn't send you off into Never-Never Land. Maybe even a first order solution if you're good.