The rationale to limit yourself to only a carry-on is to force you to travel light for the purpose of ease and mobility, and to a lesser degree to avoid a lost bag when you arrive.
Certainly picking up things is going to happen, not a problem as long as it is within the limits of what you are able to handle. Times that we had a "Home Base" type of travel, we could accumulate much more. If we were constantly on the road and had to carry everything, we keep it light, maybe picking up a few things toward the end of the trip.
As for checking a bag, we always check bags on the way home, why not? even if it were misplaced, they will get it to you in a few days or so, if at home, not a problem. We also usually pack a soft sided bag, a duffel or I have a RS backpack type bag, and use those for extra things and to check on the way home.
For breakables, packing in one of my sturdier bags, using dirty clothes covers most of it. Sometimes I will pick up some bubble wrap along the way if needed, if I were to get a larger volume, then I would look for a place that could pack items in a box and then check that.