What I have seen is that the parts that come with typical kits are WAY more advanced than the race cars, castles and pirate ships I used to have. I'd say a good percentage of the bricks used to be bricks I'd only see in the advanced Technic kits from back in my day.
I will say though that I went and bought a bucket of generic bricks because a lot of the bricks that come with the standard kits today aren't super awesome for a four year old that wants to build simple buildings and stuff like that.
http://lego.wikia.com/wiki/Classic
The large, multicolor set runs about $48 in stores.
Even the specialized sets have a fairly small share of specialized pieces, and they still sell generic, non-specialized sets.
Plus, even the “specialized” pieces are (by design) easy to repurpose.
This was about 1980, by the way.