SQL Server: Do Statistics Updates cause query plans to be flushed? Should they?
The answer is close to your "stats updates automatically cause dependent query plans to be flushed". They don't "stick around"


Flushing a plan from cache is determined by memory pressure.
Statistics updates cause plan recompilations if AUTO_UPDATE_STATISTICS is on.
Updated statistics only mean that individual statements in a batch plan need an optimality based recompile, it does not flush the whole thing.


The analogy might be separation of concerns: the stats thingy does stats, the plan cache widget does plan cache stuff. Statistics says "I've changed", and the consumer of this status decides what action to take: not the generator of this status.

See Execution Plan Caching and Reuse on MSDN.