I'm all for it, it's what other people should do.
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I worked for a company in the late 90's that introduced an incentive programme for car sharing, I teamed up with a fellow who lived in the same village as me around 20 miles away from work, another lady joined who lived about 5 miles further on down the same road. Initially she drove to our village then we alternated between the 3 cars as to who drove the rest of the way.
Inevitably one or other of them overslept/had a childcare issue/was ill etc. etc. meaning we were usually half an hour late into work. Then the other chaps wife got an evening job so he had to be back at a certain time to allow her to leave for work so we all agreed to work through our lunch hours and finish earlier.
My work mainly involved maintaining equipment that had to be in service the next day, prior to car sharing I could always stay late to finish, the need to be away on time to accommodate the other two meant that I often couldn't start jobs that came in less than an hour and a half before finishing time as I couldn't be sure of finishing them meaning often the last hour of the working day was wasted.
Add in the inevitable one person has to rush off early due to illness/childcare/whatever...
Very soon we gave up and all went back to independent travel, almost everyone else who tried it did too.