I am just a mathematician in finance, basically a brownian motion specialist and what I am saying might not be of any interest for you.

However it is worth noticing that far out of the money vanilla options are directly used in the hedging of exotic European options.

This is due to the Peter Carr's theorem which states that the price of every C² European payoff functional can be replicated as a weighted sum of vanilla options at different strikes (including far out of the money strikes). What is beautiful is that you heve a direct exact hedging of the option without making usual greeks hedging.

This can also be extended to interest rate options as a weight sum of vanilla caps/floors.

And I know for sure that a few years ago some banks did not understand why major banks did sell such far out of the money options and it was because of the above mentionned reason, that is the hedging of exotic OTC options.