Everyone run blitzes on early downs, first off. It's usually a check or series of them that relate to formation/down/distance and nowadays probably statistics as well (gameplanned for that opponent obviously). We did a ton of that vs the 9ers for example and I'm willing to bet more than Cincy did in any of their games.
But specific to running the ball in shotgun I will say you need some things to really make it work. First you need a back who is comfortable with that type of handoff. Some backs need to be deeper with the field of vision and/or aren't comfortable with that type of handoff in terms of maximizing what they can do. Secondly it's more potent if the RB is a great pass blocker, and this is magnified even more if you delay the handoff which forces the defense to play their pass call. This is why I keep saying we should run draws with Michel because everyone knows he's a fucking tank in pass pro. Then of course you need good OL or there won't be any room to run but that sort of goes without saying.
One other thing is both the Bengals and Rams are deceitful in what they do, in terms of how it is presented to the defense. McVay's illusion of complexity line applies here. So I don't think running a ton of run blitzes is wise vs either of these offenses. And when you add on top of that the fact that both these teams prefer to throw the ball, well, I feel like the run blitz option is only gonna be useful in those obvious situations.