B-crat is being undersold as engine fodder. First let's start with Chapel. Chapel/B-crat is a perfectly fine opening, if you are lucky chapel shows up on T-3 and B-crat on T4 so you can kick back a green on the other guy. Once you are even remotely thin, adding a Silver on top is not that harmful. Once you are truly thin, then any village and draw can let you draw and play each turn; which is particularly nice as B-crat is one of the most action efficient efficient sources of cash after his third play (sure things like Mint can compete but virtually all of them cost more and lack the attack). In the late game, having a silver on top is very nice if you are duchy dancing and the "-1 card token" is extremely handy when it eventually causes the opponent to miss when they fish with a village when they otherwise would not.
But what about other engine setups? Well take Remodel (or a lot of its cousins, like Butcher or Expand), once you have a deck drawing engine, Remodel + B-crat is a nice shiny new $5. So I carry around another village, that is less harmful than a potion and a University is not particularly bad. Or take something like Remake, once everything is gone, throwing in B-crats with a spare $4 is a nice option for gaining Remake fodder, even if it is just Remaking S -> B-crat -> $5 (duchy). A mid-game B-crat can work out very nicely for efficient engine building is the silvers are rapidly turned into useful $5/4/6 cards. Upgrade, or even Develop can work as well if you have something nice at $4 .
Even some of the other TfB profit from a nice supply of cards with a decent attack - Apprentice, Forge (particularly for quick Plat building), Trade route (particularly when you need two buy two cards for several turns in a pre-thinned deck), Bishop (disrupts the classic golden deck and provides something for the Bish to kill that isn't your own green if you need to keep it alive).
So where does B-crat falter? When draw is harder to come by than actions. If you are building a X-roads engine, B-crat even though it has high odds of hitting the other guy takes up 1 of 3 vital terminal slots and is rarely worth it. On the other hand, if I can Altar a Stables every turn, adding in Silvers is easy to manage. B-crat adds $2 buying power/turn but it also increases your draw burden by 1. Silvers are only 2/3rds the density of golds and that is a real thing ... but when draw is cheap B-crat works nicely. Another reason B-crat falters is that before you have your engine up his payout is a turn later at a time when there is quasi-exponential returns on payouts and because he is anti-cycling when you typically want it.
That is a lot of B-crat/engine games where B-crat is a skip, but I am increasingly convinced that a lot of better play occurs when you read the board for how scarce +action, +cards, +gains, and +time actually are. When +cards is cheap and other things are expensive (or otherwise impossible), B-crat is a lot more manageable than let on. Sure most of the time, +cards is the hardest thing to mass (hence why its token event is the hardest to play), but likely a good 10-20% of boards do actually go the other way.
B-crat is not something that works well alone in an engine, but with a good enabling setup (e.g. village/Workshop/Smithy, Remodel/trasher/power non-terminal $5s) B-crat can do well either to degrade the other guy during the trash everything phase or to rapidly build value during the mid-game. Often this makes B-crat tactical - are you in a point in the shuffle where a spare $4 gain comes up with a nice action balance? But that is still a lot more common than the the ignore it in engines mentality showing up in this discussion.