I don't know if this is true for all carts, but many of them have huge holes where a kid would put their legs if they sit in the top part. However, unlike back home, there is no flap to cover the holes, so a lot of things could fall out. If this isn't why, then I'm clueless.

I also never questioned, so do not know the real reason.  But it will be my guess that they use both, basket and cart, to keep things separated.  I do have noticed that some place for example meat, or fish or whatever, some vegetables, and other eating products in basket, and basket in car, while placing other products directly in cart.  Or viceversa.  Again, to me is not to be selfish, but the way they think.

Yet, at check out, everything is mixed together.  I dislike the basket, I always use a cart so I can push on those standing in front of me blocking the aisle while deciding what to look for next.

Well this thing is not so evident everywhere in China, as I have seen from my travels over the years. There is a group who prefer to use only basket(easier to get rid of when done shopping),only trolley (heavy duty) and the topic of this ques. the very dumbtastic trolley-baskets. They feel they can seperate the vegetables from the other things (no point in doing it as the vegetables have their own bags), the easier escape method if during their shopping time feel they need to only buy a few "essential" things which can be carried by hand and dump the trolley somewhere off. The final reason could be over ecstatic about shopping in a Mega-store/shopping mall/ Walmart/ other big shops. 

The main answer for why is the same as why they will shoot snot rockets or just throw trash anywhere.  There is no social tact.  Outside of their own home or car is outside of their realm of caring.  So if they used three shopping carts to buy two items, it wouldn't matter.  You not having a basket or cart isn't their concern and walking around with extra carts could make people think they are richer and more important.