Thanks for the quick and useful comments. Here are some replies and additional information.

There are some multi-tools that have chain breakers. There is the Topeak one noted by a commenter. Crank Brothers has another. They don't sell the chain breaker separate from the multi-tool. I like my setup of a separate ratchet wrench and standard-sized 1/4" bits. Using the hex keys, etc. on a multi-tool would be slow and frustrating, and wouldn't give sufficient access to some bolts due to either the bulk of the multi-tool or short reach of the hex keys. So, adding a multi-tool just to get the chain breaker would add bulk and weight to my setup without adding utility.

The Wolf Tooth Encase has a chain breaker, but it only comes with a plug tool, which I don't need since I prefer tubes to tubeless. They also have a chain breaker that comes with a utility knife. The Encase weighs 46g, which is lighter than the Park Tool chain breaker, but looks like it could be a little fiddly to install in my drop handlebars. I don't need the utility knife, and that tool weighs the same as the Park Tool chain breaker. Wolf Tooth is pretty good quality, so I'll think about the Encase.

By the way, Topeak also has a chain breaker that goes in the handlebars without the other multi-functions. It weight 52 g, so is a little heaver than the Encase but a little lighter than the Park Tool chain breaker. Like the Encase it would move the bulk of the tool to the handlebars, and may be less fiddly than the Encase system. It's not cheap.

One downside of any in-the-handlebar tool is that I ride a couple of bikes. If I want the tool available on all bikes, I would need to get several of the tools so I could install one in each bike, or swap the tool each time I change bikes. That having been said, I don't typically take a chain breaker with me when I am on riding in town. So, this may or may not become an issue.

I have an 11-speed chain. Good point that I should make sure whatever solution I go with can actually punch out a rivet on a 11-speed chain. I know the Park Tool chain breaker can do so.

I carry a couple of quick-links. If I have to remove the chain for some reason, such as to replace it, I use the quick-link and use some Wolf Tooth masterlink pliers to loosen the quick-link. The chain breaker is for (1) shortening the chain if I replace the chain in the middle of a tour due to wear or damage (a new chain is never the correct length), (2) cutting out a bad link of a chain if it gets damaged, and using a quick connect to rejoin the chain, or (3) if a derailleur becomes inoperable, letting me remove the nonfunctional derailleur and shorten the chain an appropriate amount to make the bike a single-speed chain and bike until I can get to a repair shop to replace the derailleur and chain. I've never had to do #2 or #3 in the field, but I almost had to do #3 once. Fortunately I was able to get the derailleur working before I actually cut the chain.

I'm looking at the Topeak multi-tool. It looks a little bulky. It weighs 62 g, so the same as the Park Tool chain breaker, but would let me not bring the Wolf Tooth chain pliers, which weigh 39 g, so there would be a net savings of weight. The Lezyne multi chain pliers look nicer and seem to be better quality than the Topeak, and are about the same weight and cost, but are less bulky.

Back to my original question: any comments on the idea of cutting a small stand-along chain breaker to remove the handle, and using the pliers and wrenches I otherwise will have on a trip to hold the chain breaker and turn the pin? Thanks for your thoughts.