I do not own one.
I see the absolute utility, but do not understand the need or want here in Germany (which is odd as they are common, and commonly produced).
Here is my expert opinion.

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1. They are never in the correct combination of cartridges or shot shells that you would actually want. For the hunt you want to do.
A 7x65R and 12 or 20 gauge would be ok for roe deer. And maybe you could do a close range fox with the shotgun. We don't normally get to hunt birds in Germany during rifle hunts.
2. They are heavy, some are crazy heavy.
3. They are expensive, a new drilling is a 10,000 Euro prospect on the bottom end. Used drillings have issues, the sub 2000 Euro used drillings start having serious issues.
Here are some ideas though. With my 2 cents.
A mountain gun: Bockdrilling in 30 Blaser or 8x57R or 7x65R, 2nd barrel 5,6x50R or 222, and 20 Gauge. If you hunted Austria for grouse and could get a spring roe buck or gams (chamois) open in May or April during your capercaillie hunt. This would be a good option and wouldn't be so crazy heavy. This would also work really well in Southern Sweden, Finland or Norway doing the same hunts but in the winter, plus moose, reindeer and stags.
I would never want one for a driven hunt in mainland Europe, unless you were shooting foxes in the face at your feet. Then I would want a 9,3x74R double rifle drilling with a 20 gauge barrel below it. This would be great for driven hunts. Plus give you a shot gauge with 2's or 4's for foxes. But since I mostly hunt federal lands, foxes are protected. So this isn't happening. I prefer a straight pull or a pure double rifle. Or a Browning BLR would be awesome.
Everyone that I know that has one has specialist rifles that are better at the task at hand.
1. a lighter rifle for the mountains.
2. a faster rifle with more versatility for for driven hunts
3. a more powerful rifle for red stag rut.
My buddy who is an agent in Austria and hunts all over the world only uses his combination gun on predator hunts, and only because he fitted night vision to it.