I can't simply tie one battery's negative pole to the next one's positive pole because when the charging circuit kicks in, current will flow all over the place between them. It just won't work.
That's not really true. When was the last time you charged a car battery (which has 6 cells) with a charger with 7 battery clamps?
Assuming that the battery is manufactured properly the cells should have an equal resistance between them and should charge evenly. When cells do NOT have an equal resistance or state of charge then cells with a lower voltage should charge more quickly than a cell with a higher voltage. Everything should stay in equilibrium -- although it may require longer charge times / trickle charging to do so.
Yes I do understand that it is typical with lithium polymer batteries to control the charge in each cell individually. It's just a matter the economics of the situation where a more complex / more expensive charger makes sense.