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This logic kind of falls flat, since Tengu Dai Shogi does the same thing with hook moves and Lion Dog moves and is still considered a Dai Shogi variant.

Considered by who? In my eyes it is more a hybrid. It keeps the pieces from Dai that were in Chu, but the large Shogi variants all do that. The pieces that distingush Dai from Chu were all thrown out. Although one might argue that the promotion-on-capture rule is the decisive difference.

But of course there is nothing against hybrids.

Buddhist Spirit is also an interesting power piece. I think the more important question is whether (some of the) power pieces should be subject to some anti-trading. In original Dai this was not the case, but that could be one of the reasons it was replaced by Chu in terms of popularity. Tenjiku Shogi also has no anti-trading rules. But I actually played that, and even after trading away the Fire Demons and neutralizing the danger of the jumping generals it remains an enormously tense game, because you can get back a Fire Demon through promotion. Which creates an immediately winning imbalance. The Water Buffalo's themselves are only average pieces (by Tenjuku standards), and are not easily traded. So equiping some less important pieces with decisive promotions might be an alternative to anti-trading for keeping a large game exciting.