I went to the fix it kit link Cycclocommute provided, and that fix it kit was 20 something dollars, not a relatively expensive purchase compared to good multi-tools.

Yes, if a side plate of the chain cracks, or a pin comes loose from a plate, I wonder if it's even possible to pry the damaged link plates off the chain. 10 and 11 speed chains have the pin ends mushroomed like a rivet. I think it would be extremely difficult to remove the damaged link. Perhaps a 3mm hex wrench used as a lever to bend them apart?

I've only even heard of a broken chain once in the last 5 or 7 years. They seem pretty reliable.

Using a tiny chain tool on 11 speed chains
Do those miniature chain tools on a bike multi-tool work on modern chains? I've never tried one.

I have a small Park CT-5 tool. It worked okay on 10 speed chains. But it's very difficult to push out an 11-speed pin. I had to hold the loop handle with an adjustable wrench to get more leverage.

So I got the larger, sturdy CT-3.2 tool. This is much easier to use, at home.

You get 'upset' ends, (you call mushroomed, its more subtle that that),
of the chain pins out
by stretching the hole in the outer link plate.. that is pretty much why
you only shorten a modern derailleur chain..

I tried breaking a few chain segments with a little Fabric 16 multi-tool just now, for the sake of science. The Fabric 16 chain tool is pretty small.

Ultegra 11 speed was cake. The mushroom pin popped right out. Just about any reasonable multi-tool should suffice for this chain.

A KMC 1/8" track chain didn't even flinch. I thought the little tool was going to break, Had to give up because my fingers hurt.

The CT-3.2 is a good shop tool but I got one with a bent tip from the factory.

-Tim-

I use a topeak hexus II that has a chain tool and levers, keeps everything in a compact config in my jersey pocket for saddle bag

Is it not possible to extract all the pins out of a masterlink chain such as 11-speed KMC by using a chain breaker, like you can with a shimano chain? If so, does that mean you can't re-lengthen a masterlink chain, except by using in a second masterlink?

if you didn't use a shimano specific pin that is a ticking time bomb

Yes, technique is the key. I have only messed with KMC 9sp chains, though, but once you have practiced a bit it becomes reliably possible to remove the link.