Ink carts have a hard existence from the manufacturer to the vendor, and from the vendor to the printer. It’s possible but illogical that they would become fragile once put in service.
Both the cart and contents are designed to tolerate being shaken. At worse (unless someone is throwing the cart against a wall or something), some air gets mixed in. Let it stand for a while and any bubbles will dissipate. Plus, with every cart I’ve seen, the ink is drawn from near the bottom, so air isn’t likely to be there long in any event.
As you pointed out with a clogging printer, at worse one can replace the cart and the problem will resolve itself, so no real risk.
Not tryin’ to squabble, just pointing out what may not be apparent.