People like 5e, and so use that preference in place of actually analyzing the system and then you get arguments that 5e does heists just fine when, in reality, it's doing so because of the work a GM is doing to hold together play the system doesn't do anything for. Simultaneously, you get statements that use dislike for a system to dismiss the support a system has for a thing.
Bluntly, 5e has no support for heists. Blades has lots. You can still prefer to ad hoc with 5e than use Blades, and that's just fine.
This is true but you're kind of doing it yourself by claiming 5E has "no" support for heists.
D&D has no rules that are specifically designed to support heists, but it does have a lot of general purpose rules which support heist-based gameplay. So claiming it has "no" support seems excessive.
Equally, claiming BitD has lots of supports for heists is somewhat misleading - it has a lot of support for a highly specific cinematic approach to heists.
If you narrowed your claim to "cinematic heists" (i.e. ones where the pre-planning isn't shown in detail, only possibly as a montage sequence or the like), and said D&D doesn't support that, and BitD does, you'd be right, but I think that illustrates the problem. Overly-broad claims.
I think of horror as more of an atmosphere thing than a mechanical thing, and I can do horror by description/s, not even rulings. Is it possible we have different ideas, here?
I think we've getting closer to the point here.
D&D does not have any inherent mechanics which support horror-based play. It has certain mechanics which go against horror - specifically levels and HP, and the extremely powerful magic PCs can routinely wield, which tends to allow PCs to "just say no" to a lot of horror situations.
Whereas some other RPGs do have mechanics which explicitly support horror-based play, and have no mechanics which go against it.
But obviously horror isn't just rules - it's also about description and everyone buying into the atmosphere and so on. The issue is that when you're relying on description and buy-in as the sole generators of horror, it's like a soap bubble. It might not burst. It might even land on a surface and sit there for minutes or hours (I mean, okay, this is a tough soap bubble, but stay with me lol!). But it's very easy for that horror bubble to be burst by D&D's mechanics, esp. if even one player isn't buying in or was but reverts to normal D&D play under stress or forgetfulness.
Whereas in games where the mechanics also support horror (and/or don't contraindicate it), then it's more like a slightly under-inflated balloon than a soap bubble. It's a lot harder to burst. It naturally tends to stay together. Hell, some horror games are so well-designed they sort of automatically get people back on track if they temporarily veer off course, because the mechanics innately support the theme.
But can you do horror with D&D? Yes. It just tends to be a lot more fragile and rely more on buy-in, and also on the DM very carefully picking the monsters and so on.
With 5E specifically I'd say it works a lot better at lower levels, because once you get to a certain point you have so many HP and spells and fallbacks that even scary-ass monsters tend to have to spend a lot of time messing with you to do anything, which diverts things from horror to mechanical challenge.
EDIT - As an aside, it's interesting to compare say, Earthdawn to 5E in terms of horror support. ED basically has levels, kinda-sorta has HP, and whilst its magic is never as powerful as D&D, it's pretty common. But the issue is, ED was designed to support horror, so the enemies have more ways to mess with PCs, the PCs have less absolute defences, less ways to say "Just no..." to stuff, and the level/health gain isn't arranged the same way as D&D, so it remains pretty horror-friendly the whole time. Plus there's the, well, Horrors, who are often designed in ways to be specifically horrifying inside that mechanical scheme, where many "scary" or "horror"-themed D&D monsters are merely mechanically challenging and have little/no mechanical horror component.