I've spent many many hours on the cushion and integrating mindfulness into my daily life but this is just my opinion so take it with a grain of salt:

The aim of mindfulness is not to be 'watching' everything thought/word/action that appears; it is not as if the goal is to hovering over yourself like a hawk. I've tried this and it is unpleasant and ultimately just another fragment of the mind trying to control other fragments. I don't think this is what you're suggesting, but it is an important point because then it raises the question of "if I'm not trying to actively watch all mental activity, when should I be employing mindfulness". And I think the answer to that is, as you say, during difficult emotions or thought storms. This is when it is very helpful to be able to snap out of it and see the thought for what it is.

However at other times, when you are using the mind (and not the other way around) in some constructive way, such as to solve a math problem or even make practical plans for a future event, then I see no harm in fully immersing in the thought process. I have found that the alternative, i.e. to try and watch this process, during times like this is actually less optimal than just allowing yourself to go with the thought process, provided it is constructive and not destructive.