Domen
Misico dux Vandalorum
I'm not sure if such a suggestion is even necessary when modern humans were more numerous. At any rate if Neanderthals were for mysterious reasons less fertile or more slowly maturing, this would have to show statistically in modern humans with shown Neandertal ancestry.
In modern genomes Neanderthal ancestry is not evenly distributed, but some chromosomes and genes have more, others have less. This is due to natural selection - some traits inherited from Neanderthals were being selected for, others were being selected against. Due to this reason it is also impossible to reconstruct a 100% pure Neanderthal even if you take DNA samples from all living humans. Some parts of Neanderthal genome were eradicated in the process of natural selection, while others were promoted in cold climate of Eurasia.
BTW - speed of maturing and fertility rates are also related to things such as diet, living environment, and culture.
Or simply because modern humans were more numerous and better adapted. What's with this breeding preoccupation?
Modern humans were not better naturally adapted to Eurasian climate.
Neanderthals had been evolving in cold climate for over half a million years, while humans just arrived from much warmer environments.