Here in the USA currently the most popular "take down" rifle is the AR-15.

Push 2 pins and the thing comes right in half. With a 16" barrel, and with a flash hider installed, the whole thing will fit into a case only 25" long.

In many places a "Military style" semi-auto is illegal to hunt with, but it is fine in most of the USA. ARs can me made in 204 Ruger 223, 6.5 Grendel, 6.8 SPC, 7.62X39, 300 Blackout, 458 SOCOM and 50 Beowulf. Accuracy is very good and reliability is fine too.

The only problem with them as far as hunting goes is that they just are not as "cool" as the old classic guns, but if coolness is less important than utility and compactness, the AR is probably the best over-all take-down rifle yet invented for most American game.
Power is available from the 204 to the equivalent of the 257 Roberts, to the equivalent of the 45-70, and to the equivalent of the 50 Sharps.

For a take down rifle that shoots a cartridge from 270 Winchester up to the big magnums (long range hard-hitters) I am betting the only answer available today is the above mentioned Browning BLR, or a semi-custom or full-custom made rifle.

I have made a few in the years past on Mausers and one on a short action M-77 Ruger. Any good smith can make you one.

However thread wear is a potential problem, so I like the idea of sights which should be soldered so they can be heated and moved to 12:00 if ever they need to be. I do not know if such a concern is really well founded. Of the rifles I have made in the past none have needed adjustment yet. The first one I made for a man was in 1983 and it's still fine.
However it is only taken down when it need to be for transportation which he tells me is only about 5 times a year. So maybe such things are not as big a concern as I think they are.

The first one I made is also a swap-barrel job with one barrel in 300H&H and the other in 375H&H, so the wear is divided between the 2 barrels to some extent.

Fun subject. Lots of ideas to play with.