In my opinion, no, looking at each taxonomic level is not necessarily valuable.
But it depends entirely on your question, of course! In my opinion it is most informative to look at ASV and species levels, perhaps also genus/family (again depending on your question).
I would let this be guided by a specific hypothesis, e.g., are you actually interested in genus/family level differences? Looking at higher levels, e.g., phylum, may not be suitable unless if you have a focused question, as discussed here:
Times have changed I suppose — the analyses that developers deemed useful in the design of qiime 1 (a decade ago!) are not all state of the art in 2020. That is not to say that it is wrong per se, just that the field has evolved and it is recognized that, e.g., phylum-level information is often not revealing... and ASV-level analyses are now possible.