I think overall cycling supplements is a prudent approach, with some exceptions always. To answer your query:
in most cases i.e. in favor of cycling:
a) you stimulate/support your cells to do work and/or change their behavior, instead of making your cells get accustomed to a constant application of an exogenous stimulus i.e. the supplement.
b) it is actually just like dog or child training. Your cells are like you, or little tiny versions of you. In the ideal world you don't want your body to start depending on the substance permanently, your goal is to coax the body into making its own substances in the long-term.
c) Realize that this world is false. Everything has a 'bias', nothing comes without it. Usually in a forum like this, you have people like yourself, and we have our own biases, hopefully which is to help each other 'heal' and to err on the side of caution. On the other hand, (and not to berate) stakeholders that make living by selling supplement products, it can come natural for them to have a bias to take a product daily, advise others to take it daily, more the quantity - merrier be the outcome.
That said, there would be plenty of exceptions to the above general rule:
a) sometimes, all the above is just not a choice. e.g. it is a pharmaceutical medication whose efficacy is only studied while being taken on a continuous daily basis, or when doses are skipped could have deleterious effects.
b) Supplements can fall in this category as well. e.g. you experience a bacterial infection. You would not want to skip days as that is akin to creating "bacterial resistance". You would want a regular exposure of the substance to the bacteria, daily/twice daily etc, until elimination of pathogen. Anti-biotics (pharmaceutical or natural) fit this category well. In other words, when experiencing an outbreak (of some pathogen in your body), you would want a steady/regular approach of using that supplement i.e. prevent pathogen resistance to that compound.
What are your bases for saying cycling off can improve the immune response to the stack ? I keep seeing online recommendations to take such stacks every day.