Why is 1 satoshi the smallest division of a Bitcoin, and why is it important that 1 satoshi cannot be divided any further? Could there be a viable system where 1 coin can be divided infinite times?
It is by design. Satoshi Nakamoto decided that Bitcoin should be divided. I think he foresee that the prices would become much higher.
Dividing a coin infinite times can not be feasible, there should be some limit. Otherwise it will be very hard for current computer systems to process those data.