In relation to the cola wars, compare the historical profitability of
"concentrate producers" and "bottlers". Given that concentrate
producers are so much more profitable than bottlers, why would they
want to vertically integrate into bottling?

couple things: 

the bottlers weren't always separate from the concentrate producers,
so you'll have roughly 15-20 yrs of data.

second, it's more than profitability: bottlers have much lower return
on capital (op income - taxes / invested capital); they're more
capital-intensive and have higher fixed costs...  the concentrate
producers can control the bottlers almost as if they were their own
(think restaurant franchisees), without taking on the additional
capital.

Think of them like hotel management and hotel ownership?  Companies
like Marriott broke themselves up into two different operating
companies (management and real estate) to reflect the very different
economics of those two businesses.  The resulting "purer" economic
statements allowed investors to more accurately value the two distinct
business models -- thus lifting the overall value of the "combined"
entities.  Mashing the two models together caused confusion and thus
lowered the values.

In terms why you might want to own your bottlers?  They control the
distribution and you are dependent on them ultimately driving your
concentrate sales.  Consider  when Snapple came on the market.  A
bottler would not have the same incentives nor the same deep-pocketed
resources as a concentrate company to fight a battle with a new
entrant.

By standing by and watching the bottlers do nothing (because they had
no money to do anything) concentrate companies lost shelf-space and
market share to a relatively unsophisticated new competitor.  You
don't want to get caught in that situation again.  My thougths,
anyway.