why no bracha on sukkah on shmini atzeres

Rav Kasher has a beautiful overview of the Rogatchover’s thought in the intro. to the Devarim volume of the Rogatchover al haTorah where he presents some of the classic chilukim and conceptual constructs of the Rogatchover and gives examples of sugyos where these ideas can be applied. It is similar in content to the amazing Mefa’aneyach Tzefunos. One of the topics he addresses is why we sit in the sukkah on Shmini Atzeres but do not recite a bracha, unlike other mitzvos performed because of sfeika d’yoma which do warrant a bracha. According to the Rogatchover (into p. 22), dinim d’oraysa tell us about the halachic nature of reality, i.e. they are dinim in the cheftza; dinim d’rebbanan impose legal obligations on the gavra (see post here). The chachamim can impose a chovas hagavra to sit in a sukkah on shmini atzeres, but cannot create a halachic cheftza of sukkah once sukkos has ended. Without a cheftza shel sukkah, no bracha can be recited. (See this post where we discussed a similar distinction of the Rogatchover between eating in the sukkah as as a kiyum of defining the cheftza shel sukkah as a makom dirah vs. the chovas hagavra to perform the act of eating only while in a sukkah.)

I heard a different answer to this question in the name of R’ Soloveitchik that also uses a classic Rogatchover-ish sevara. When two halachic categories overlap, the result can be either a harkavah shechnit, e.g. the two categories co-exist side by side, or a harkavah mizgit, i.e. the two categories combine and form a new synthesis. For example: the halachic status of a chatzi eved chatzi ben chorin might be the same as the full status of eved and ben chorin overlapping and co-existing, or might be a completely new status that is a synthesis of both elements (see Avi Ezri, Hil. Pesachim). Another example: bein hashemashos may reflect overlapping states of day and night, or might be a new time status that contains elements of both day and night (see Shiurim l'Zecher Aba Mari). R’ Yosef Engel in Beis haOtzar similarly discusses whether yamim tovim which overlap with Shabbos have two seperate two kedushos hayom which co-exist, or whether there is a categorically new kedushas hayom formed from the combination of both. R' Soloveitchik applied this same chakirah to Shmini Atzeres, which is both a holiday in its own right as well as an extension of sukkos because of sfeika d’yoma. Instead of viewing those two identities as co-existing side by side, a harkavah shichnit, R’ Soloveitchik viewed them as combining to form a new unique halachic identity. This new synthesis kedushas hayom is not the same as the normal kedushas hayom of sukkos and therefore does not obligate reciting a bracha on sukkah.