Agreed, they are often filthy.(Plastic baskets appear to be much dirtier than wire. They often have visible smears of various unidentifiable substances. They should have a basket washing machine!)
On your main point, there's no doubt that basket self checkout, which is very common in major towns and cities where supermarkets are often larger, is very popular.
In the large Sainsburys I use there's 20 self checkout stations in that compound, 10 Cash or Card, 10 Card Only and often more than half of all customers checking out are using them, even queuing to do so. Clearly using baskets restricts the amount they can buy, often my basket ends up painfully heavy before reaching the checkout area, so they are likely to want us to use trolleys so we can buy more.
Some cheekily bring trolleys into the basket self check out area, clogging up the system, but only a couple can do that at most due to lack of space in that compound.
They did at one time have two trolley self checkout lines next to the staffed trolley checkouts, but they operated too slowly as people recorded a trolley full of content, so they scrapped them.
There's no doubt though that self checking out is the most favoured way of all, only limited at present by insufficient space and the machines provided for it.
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