I think one could easily make a stock lever action that was good enough for the task of taking large dangerous game. The reasons it has not been done have been largely identified. Back in the early days of smokeless powder and bolt actions, they so distinguished themselves in Africa, from the Boer War, to the game fields that there would be little reason to look for anything else other than the double rifle, which was obviously very much in use. The US did not adopt bolt actions as quickly, and after their brief appearance at the front in WWI, they had by WWII sensibly moved strongly in the direction of other action types. Of course bolt actions are very popular in the US, but they didn't blanket the game fields in the same way. Even mid way through the last century a hunter in the US might well still be shooting a lever. So you have the lever being important outside the dangerous game fields.
The Winchester was used by the Russians in WWI and worked very well by some reports, being preferred to bolts when the individual soldiers could get them. So chambering them in a 9.3x62 would have been easy enough and they could have been side by side with developments. A local store has barrels for the Garrand in 9.3x62. That could be another thread, why not semis.
I shouldn't draw this cultural distinction too strongly. There are pictures of Settlers in Africa with lever action rifles...
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I think that one of the reasons that big bore levers have not become more available is because of the 45/70 myth. There are many big bore levers being made today, maybe more than at any time. And a lot of this appeal has to do with the universal acceptance that levers are a great platform for 45/70s, and that the 45/70 is magic. This mythical performance of the 45/70 is basically true if you live outside of Big Five country. So you can't blame folks for not wanting more. But for those of us who want more it is very hard to get, particularly outside of the US. The 50 Alaskan has also flagged as far as I can tell without access to actual sales statistics. It has never been offered in a stock 1886 that I have seen, and many of the people who were offering it a few years back, have stopped, offering it in the Mossberg customs. A better choice for the US based shooter is probably the 470 and 475 Turnbulls, because they absolutely stroke the ballistic minimums. These are readily available from Turnbull but so far I have not seen them from others. The Turnbull rifles are excellent, but they lean towards nostalgia over practicality, that is just his niche.
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I don't think that the lever offers anything that the Blaser or doubles, and maybe even the best bolts can't do better. Basically it comes down to fire power. The Blaser is a stock item in the 500 Jeffery, and second shots are probably fast enough for clients, or the best professionals who might be better off with a double. When they wade in, it can be so tight on time, you really need a double, 3, 4, and 5, are probably not going to get used in every case, and if you have that much time, you can probably get by with a bolt. Most of the levers can be locked up and clearing can be a problem. Again, that is probably something that could be changed in the design, but until Blaser decides to make it happen, we are probably out of luck. Currently my local shop has several Blasers in 500 Jeffery, new and second hand, and not a single super sized lever. Getting one would cost more than the Blaser, or even a custom bolt gun.
