Taking this idea farther, there are a lot of cases where processing doesn't have to immediately be transactional. The transactional can be delayed in a lot of cases.
One accutely relevant recent example has been the recent naked shares scandal which helped sink the US banks much faster and deeper. These naked shares are when brokerage houses sell shares of a company that they don't really have. Normally a brokerage house would be transactional about buying and selling, but in this case the brokerage house can sell without actually owning the stock and buy the stock later. If the risk of this kind of inconsistency is smaller than the overhead a slower more expensive system insures consistency then why not go with the inconsistency?
Of course in the case of the brokerage scandal the inconsistency might have been intentional and if so and if regulated would bring back a transactional system. There will always be the requirement for transactional systems guaranteeing the usage of relational databases.
Interesting article on the subject (including quotes from me)