Typical intersectivity is shown here, at least on the surface. I don't think anyone would argue with the equivalence
'Aloysius is a mad scientist'
=
'Aloysius is mad' and 'Aloysius is a scientist'.
Compare 'This is a valuable book'.
But 'He is a heavy smoker' is not equivalent to 'he is heavy' and 'he is a smoker'; only the second statement is necessarily true.
And 'he is a former president' certainly does not mean that he is still president, and 'he is former' makes no sense.
[Adjective] + [noun] phrases behave differently.
..........
A complication which the original example brings out nicely is that 'mad scientist' is at least a strong collocation ... though I wouldn't insist it was a compound. This means that it behaves to some degree (totally, for compounds) as a single element.
He is one of that recognised, stereotyped set, {mad scientists}.
With compounds, analysis is unfeasible:
- This is my walking stick.
It's not walking. It's a stick used to help one walk.
And, whether 'mad scientist' is a strong collocation or a compound, it's obviously ludicrous to associate 'mad' with 'science' rather than 'scientist'. There are of course high fliers (often hyphenated or solid), but asking what a high fly is would be in the crazy vein of Groucho Marx. And there are heavy drinkers, but I've never seen 'heavy drink' for sale. Light cruisers, but no such thing as a 'light cruise'. A sleeping partner doesn't have 'sleeping parts'. A criminal lawyer should certainly be well versed in criminal law, but the Lone Ranger didn't ride the 'lone range'. A day tripper takes day trips but an inveterate biker doesn't ride an inveterate bike. A cattle rancher owns a cattle ranch but a gentleman farmer doesn't own a gentleman farm. One has to be sensible in deciding what modifies what and what relates to what in such collocative noun phrases / compounds.