One of the standard tenets of quantitative finance is that options should have an intrinsic value because optionality as such (in the sense of having more choices) should bring about value.
This seems to make sense intuitively - yet intuition can sometimes be misleading as we all know: Braess's paradox is called a paradox because here additional choices (i.e. options) can lead to worse overall performance, i.e. reducing the value for all participants.
Are you aware of (theoretic or special) situations where additional optionality in instruments of quantitative finance (e.g. some exotic options or in some pricing models) could lead to lower value?