Collapsible Luggage Cart?

In the places where it's easiest to use the cart (airports and train stations) free carts are sometimes provided. When you're not using it, it would be one more thing that you're carrying on your back. I suggest reviewing these recent discussions of the topic:

https://community.ricksteves.com/travel-forum/packing/luggage-cart

https://community.ricksteves.com/travel-forum/packing/trolley-for-carry-on

I posted this on another thread recently, but my compromise this year, instead of a convertible backpack, is this: Eagle Creek Lync 20. The wheels come off, as do the straps, so I guess it's a convertible with one extra option. I think it will meet my needs perfectly. Of course, as Laura says, once you leave town with the wheels, you're stuck carrying them one way or another for your whole trip. I'm ok with that, as I really can't haul a backpack this year, so I'll only put it on my back when I need my hands free for short periods, such as climbing into a high train. Another option to consider. When you are using the wheels, at least the backpack is securely attached, not flopping over sideways as my suitcases always did on luggage carts.

P.S. the single handle does not intrude into the packing area much at all

I did a review of the Lync 22 when it came out and looked at the Lync 20. They aren't bad but I found the 20 to really be lacking in space when actually packed.

Eagle Creek makes another line of bags, the No Matter What Duffels, that come with both wheels and without wheels. The interesting thing about these is that you can buy a detachable backpack system if you want to carry the bag on your back. I did a review of the No Matter What Flatbed Duffel 20 (rolling bag) and the detachable strap. I liked them and have used them.

I also liked the Rick Steves Rolling Backpack. I didn't think the backpack straps took up too much space but the bag is only 7" in depth. (This easily goes up to 9" if you pack more.)

As for a cart, I've tried a lot and they add weight. There is one that has a specific purpose.

Conair Travel Smart Super Mini Cart

This cart is very small. It can fit into a carry on bag sideways (the length is less than 14") and it weighs less than a pound. The downside is it only holds a max of 25 pounds, has flimsy wheels so taking it on rough terrain is a no go, will tip over if your bag is not balanced, and feels very flimsy. But if you're in an airport or train station, have a long walk ahead of you, and can't find a luggage cart, this one will make do in a pinch. It might work on city streets but that's taking a bigger risk than hitting on a pair of kings.

The following is a bit off-topic, but just in case the OP is considering this option, I thought I'd pass it on:

I have practice-packed the Lync 20, though it hasn't been on a trip with me yet. It will hold everything I need to take, but nothing extra, that's true. Using the new eBags ultralight packing cubes, which are smaller than the old ones, I fit in two large, two small and one slim, just as eBags advertised. (Full but not over-stuffed.) That takes care of all my clothes - day clothes, sleepwear, undergarments, swim wear & hat. I can fit my sandals and my flip flops down the sides of the main compartment (it's a bit wider at the bottom than the top). There's a small side zip pouch on the inside that holds my foldable hiking poles perfectly, though I'm concerned about getting them through security so may ditch them. A small toiletries kit, my packable raincoat and packable tote all fit in the front compartment. The 311 bag will fit in the small top zipped compartment. I'm not taking a camera, iPad or a laptop, just my phone, but one of them would easily fit if I change my mind. I think I'm good to go for a summer trip. Winter would be a challenge with the bulkier clothes.

I will have just this 20" bag and a small cross-body purse to manage. Since I'm traveling solo next summer, I went to all this effort to make sure I could handle my own gear. I'm confident this will work for me, and I'm sharing it to see if it can help anyone else.

I used to have a lightweight luggage cart. Nobody uses them any longer.

I prefer a ultra lightweight rolling carry on bag--20" or 21".

I had that same thought a few years ago. My back just can't tolerate a back pack, so I purchased a collapsible luggage cart. It was the biggest hassle ever. I had to use bungee cords to hold my bag on and then it still slipped off. At one point it banged against my ankle and caused a huge bruise. Needless to say I got rid of both the luggage cart and the bag. I would shop around for a good wheeled bag and go with that.

I'm thinking you're going to want to go the rolling backpack route. Yes, rolling bags do lose some interior packing space due to the handle, but you can pack smaller articles in between the handle compartments. I gather that you would prefer to roll your bag 100% of the time, if possible, but want to keep your options open. I think your best idea is to buy a wheeled bag, for the reason listed above. It's not a 100% perfect solution, but nothing ever is.