Basically, they stopped innovating lever guns about the same year the Mauser came out, and there is probably a connection there. I don't know if the Krieghoff pump is any good, but I do wonder if the relatively short list of problems that the lever has couldn't have been sorted out at Blaser or Krieghoff if they had a mind to. The lever has the advantage of providing the highest possible rate of carefully aimed fire, short of a semi; and a large magazine capacity. The Browning BLR model that seems on the way out, has a rotating bolt, and could handle magnum rounds.
As far as dangerous game is concerned, levers were used on the frontier, and today to kill grizzlies, and the 1886 can handle rounds like the 470 turnbull. Levers also saw limited military use, from which they were quickly swept aside. But they worked at one time for these things, and it seems unreasonable to assume they could not still serve today. There are indeed many who use them as carbines in policing to this day. These models never run dry because they can be stoked on the fly more easily than almost any rifle.
The Win. 1895 is one I have never handled, but apparently it has controlled feed of some description, a box magazine and will deal with 20th century pressures.
There just isn't sufficient interest to push out new designs, with a few exceptions. Even among those currently available, I am not sure that something like a well attended to Marlin in 50 Alaskan, or an 1886 in 470 is a lessor gun that a Mossberg in .375. But even if the levers meet the baseline of performance, they are likely to cost 10 times as much as the Mossberg.