I'm 42. I tend to agree with you that I dislike over-specialised pieces. But then people are creative (which is the point of Lego, after all) and they use the thing for something else entirely.
I would like there to be a few good base sets. Luckily, there are, you just have to search to find them,
I'd really like to be able to buy blocks by the kg - 200 g of 2x1, 300 g of 2x4; etc.
You can buy (or sell) any and all types of LEGO parts or sets at BrickLink ( https://www.bricklink.com/ ) . The site serves as a marketplace for thousands of sellers who maintain what appear to be fairly large inventories (tens or even hundreds of thousands of pieces).
You can find parts by condition (new or used), sort by price, filter by location (to minimize shipping costs and/or delivery time), and more. If you need more of a part that came in a particular set, you can find the set (by name or by number) and drill down to a parts list.
I've been to the lego stores in Germany and England and the "pick your own bricks" has been in all of them (although the smaller ones have fewer different types).
Lego Education does a spare parts catalog - but not sure if you can buy from it as a private individual. I used to use something similar when I was a kid - I couldn't afford (say) a complete new pneumatic set, so I just bought a pneumatics parts pack from a mail-order catalog and used those bits with my generic technic stuff.
(Another great resource is the ideas magazines they used to print - not sure if they still do - with loads of pictures of creations, but with minimal or no instructions).
I would like there to be a few good base sets. Luckily, there are, you just have to search to find them,
I'd really like to be able to buy blocks by the kg - 200 g of 2x1, 300 g of 2x4; etc.