I'd doubt that's it. Practically everything is digitally printed these days, so the complexity really doesn't matter. In some specific processes the number of colors used may be a factor, but the original design was already only two colors to begin with (or three if you count the transparent bits). The shape would matter if they were trying to make illuminated signage with the same outline as the logo which Cracker Barrel already don't do. Their pole signs at present are just rectangular with rounded corners to begin with. I'll grant there may be a minor complexity advantage to having machine embroidery done of it, but the last time I was in one of their restaurants their employees all had logo and name tag pins and their uniform shirts were sans logos, so that's a moot point anyhow.

I'll certainly concede that some C-suite idiot may think this is going to save them on uniform and printing costs but in reality it actually won't. If that's why they really did it they're even dumber than we're giving them credit for. (And another commenter below pointed out that rebrands cost money to pull off. Not just whatever seven figure consultancy fee you just paid to some twerp with a Macbook to render your logo unreadable, but also all the materials and signage you then have to get made, printed, have somebody install.)

Herewith I will prattle on about the topic because Design Is My Passion (well, okay, at least part of my job) and this whole trend obviously honks me off and I'm starting to feel like the only sane man left standing.

The rationale for dumbshit logo oversimplification I usually see bandied about is "increasing brand recognition," with the notion that a simpler logo is more readily and quickly recognizable. This has a kernel of truth to it, however only those with the pointiest of spectacles with the beadiest of chains know the secret. And that is mostly what drives this is the logo's silhouette, not the words inside it. (And to a lesser extent, its colors. But tell that to all the fast food chains who insist on using red and yellow for their branding, so that's already on the way out.) This is especially so if the logo will be seen only briefly or at a distance, for purest sake of example and for no particular reason at all, let's say at the top of a pole next to an interstate highway 200 yards away while hurtling past at 75+ MPH.

People don't read. Even so, a large portion of them probably don't have great eyesight. If your logo is going to be a wordmark, it had better have its own very distinct silhouette, and preferably it ought to be short. The frillier and less sans-serify you make it the less likely anyone is to be to comprehend it, let alone bother to process it. If your design vision absolutely cannot accommodate that for whatever reason, its surrounding geometry had better have a recognizable silhouette. And for fuck's sake, make sure it's high contrast against whatever's inside it.

I'll throw out some examples. Here are four brands who, apart from any other shortcomings and even after going through various rounds of logo simplification, still get it:

I've brutally reduced these to only their silhouettes and in the case of any that also included wordmarks and haven't already removed them from their official logo, I've also stripped them of these.

I'll bet you can name three out of four of those without even thinking about it, and third from the left will only slow down some people for a second or two.

(This is also why so many traffic signs are shaped such as they are, and the important ones don't share shapes, and also why it feels so unnervingly wrong in a Mandela effect kind of way when you visit a country whose highway authority hasn't quite figured that out.)

Meanwhile, here's a lineup of a few who fail the test:

Yes, I deliberately cherry-picked these to form a lineup of options that all suck. But in my defense, there are ever so many to choose from. Go on, whose are those? No cheating and using Google image search to try to match up the minutiae of the aspect ratios. You have to do this right off the top of your head. Remember, these are flying by on an interstate sign.

It's the same deal with app icons, which these days all seem to be devolving into "some circular swirly thing, possibly multicolored, that doesn't tell you anything about what our app does." It's even worse now that everyone's launchers seem to want to automatically badger any icons that still do manage to have a recognizable silhouette into solid colored circular backgrounds.

Heaven forbid we have both versions of the logo.