Is it awkward taking rolling carryon to the grocery store like Whole Foods, Trader Joes, etc right after a flight and before going to your hotel? Might be less awkward if in the city and near tourist areas.

The luggage is also to help carry lots of groceries back to the hotel room. I don't think people enjoy having 5-10 plastic grocery bags and haul it back to your room?

IMHO no.
 

People bring their own bags all the time to those places. I think it would be difficult managing a cart and a rolling suitcase at the same time. I would advise against putting in I purchased items directly into a suitcase. Though you definitely intend to pay a security guard might not be so understanding.

Nothing weird or odd about this. Many people arrive somewhere, including back home and head to the grocery store on the way home. Depending on the store, your bag may well fit on the lower part of the cart. Definitely don't put things into your case until you are through checkout.

I'd approach the service counter or some employee first and ask then for help with keeping an eye on the bags while you shop.

I see the occasional rollaboard or travel duffel tuggers in grocery stores and don't bat an eye.

It's fine. Don't feel awkward. People are so tired by working or passing airports that they usually don't care

This won't be unusual in any major city used to travelers without personal cars coming and going at all hours. I still might check with an employee upon entry, especially if it's a larger store or one where dragging a bag around might not be an easy thing to do.

If it's more of a corner bodega then it'll be completely normal: even locals pop in and out with small rolling carts or the bag they commute with as they do their shopping. (Again I'm assuming we aren't talking about a huge amount of luggage here.)

I’d say it definitely depends on the location of the store. The Migros right at Zurich airport? Odd if someone is not pushing around a suitcase. A suburban Trader Joe’s where 80% of customers get there by private or rental car, not so much.

I’d also be surprised if a store let the customer service desk serve as a left luggage desk because of the risk of someone accusing store employees of going through the bag

the underlying presumptions appear to be that you've either walked or taken public transit from the airport, and that the grocery store is on the way to the hotel

in similar situations I've made quick retail stops for a small number of items, but unless the store was about to close for the night or the weather was prohibitive I'd generally check into the hotel first and then return to the store unencumbered ... as noted, easy to use empty luggage in lieu of carrying multiple bags

I've done it a lot ... even when I'm not heading to a hotel. But that's almost always when I'm using public transit to get to/from an airport or train station. I've also done it when I'm using a taxi/car service to get to/from an airport/train station.

The most awkward thing about it for me is this: what do I do with the wheeled-carry-on luggage while using a shopping cart of some sort.

There is some chance that the store may flag down a person coming in and leaving with luggage as being a potential shoplifter. But at least with regard to Whole Foods, I've never seen that issue pop up for me.

Sure, it’s fine. Just use the store basket or cart for your own groceries. Pushing a suitcase isn’t much different than when I would shop with a stroller, keeping the basket atop the stroller.

it’s only an issue if a store manager (not staffer) says something negative about this.

Yeah... if you're in their with a rollaboard, then:

1. You're in a rush and on the way to the airport/train station/bus stop but forgot to buy something for the trip
2. You realized you forgot something after landing/arriving and enroute to your hotel/Airbnb you drop by a store to grab the thing you forgot.
3. You had planned to go to the store after landing/arriving to get stuff for your stay.

For 1 and 2, chances are you're only going to pick up at most a few items.

For 3, you planned this, so you've probably considered the potential challenges that may include dragging your rollaboard along while navigating the aisles with a basket in the other hand (or pushing a cart with the other hand).

now I’m picturing the convenience of putting a small suitcase in the shopping cart for Safeway/Carrefour/Aldi - then we only are pushing the cart. So that’s really not too bad :-)

Ha! Didn't even think of that one.

Not sure whether most or all shopping cars are the same/similar, but at least in many stores in NA, the full bonafide carts have the part underneath the carriage where one could probably lay their rollaboard.

Some people may get sort of grossed out by seeing the luggage in the grocery carts. Some grocery store employees may think that a bag in the cart makes it easier for shoplifting and/or more likely that shoplifting has taken place.

Speaking about reactions that I've seen happen around me.