(If answering, please assume readers already have a basic understanding of what p is in general.)
The is it pointless part of this question seems to be YES; that part of the question is similar to, and I'd guess answered by the answers to Homogeneity testing of baseline characteristics in medical trials but I'm not sure, so I'd appreciate a confirmation.
Secondly and more importantly, perhaps, the what is being tested part of the question is asked there, but isn't answered, perhaps because, as @Gala notes, a specific reference is lacking there. So that it can be answered, I now provide one (for my question), here: Table S1 at https://www.nejm.org/doi/suppl/10.1056/NEJMoa1205409/suppl_file/nejmoa1205409_appendix.pdf - from an article reporting on a double-blind medical trial.
Thirdly, and more specifically, when I ask, "meaningful?" it's because I'm wondering what the plain English meaning could possibly be of the p being just 0.01 in the chart for the subgroup trait/characteristic of diastolic BP but 0.67 for BMI (when the meta characteristics seem similar - means are ~.35% apart, ± is ~6.6.)
