Space-time tradeoff: I have an index deeper than I'd ever imagined when I started university, but everything is a search away and thus it takes time to find things and it won't be possible at all if I'm away from the internet. Cache is precious. Of particular interest is languages. You really do need to have certain things to hand when you're talking to someone in a foreign language. For most other things, it's perfe…
Reasoning cannot depend on “a search”. It is based on memory, on knowledge (not on its accessibility).
Previously if you were to opine on those subjects you would either need the information to hand, or look it up in one of a few books you happened to have near you.
The search will in all likelihood lead to better reasoning than if you did not have the internet to hand, assuming you know how to critique sources. For instance you might have forgotten some supporting evidence. This is a big assumption but it's pretty much what people should be practicing during education.
The thing you really need to practice in the modern world is judgement. You go online, read some sources, and now you have the problem of deciding which sources are worth listening to.