“Regardless, modern humans with Neanderthal in them, tend to be a tad smarter than average.”
Can you provide links to support that statement?
Regarding modern humans being weaker, I notice women tend to go for the big bad boys.
First, Neaderthals not being stupid:
In a homo sapien sapien (modern human), brain size averages 1,270 cc for males and 1,130 cc for females. Neanderthals averaged 1,600 cc for males and 1,300 cc for females
Stringer, C. (1984). “Human evolution and biological adaptation in the Pleistocene”. In Foley, R. (ed.). Hominid evolution and community ecology. Academic Press. ISBN 978-0-12-261920-5.
Second, a little Neaderthal makes you smarter:
https://elifesciences.org/articles/80757
The second point is said quietly, because Europeans/Mesopotamians have much greater Neanderthal than the Africans, who have none. But you can go look at a bell curve of IQ by country and derive that on your own.
The smart girls didn't and don't now.