I think that vada can just mean something broad like “school of thought”? Trying to think about distinguishing features of what is proposed, I guess a core idea is that there are layers or strata of varying earliness in the texts and comparison of parallels is a primary tool, though not the only one, in trying to date the layers. The abhidhamma, and certainly the commentaries, are viewed as a later layer (not directly emanating from the Buddha or even his immediate disciples) and, as such, not canonical. However, they still constituted a major project to understand and systematize the earlier layers, plus are relatively much closer in place and time, so are perceived as still having value (providing invaluable insights at times).
I suppose one cannot expect a unified understanding of the texts (more a “school of thought” regarding a commonality of approach). After all, there seem to have been divergences in understanding regarding the early texts even among the early schools with different abdhidhammas etc. (or quite different takes like the Pudgalavada, Personalists, and their pudgala concept). A commonality of approach to the early texts, likewise, is probably not going to lead to a uniformity of understanding in the present! So I guess a vada “school of thought” more so in terms of approach rather than content of understanding anyway.