I would have no problem making both the Ozeki and Yokozuna ranks slightly harder to get to as you suggested. Ozeki need 36/3 or somewhat loosened current Yokozuna requirements for 2 basho runs. Yokozuna need 3 Yusho in a 6(?) basho period, or something equally impressive. Then we'd see Kisenosato and Kakuryu stopped at Ozeki (though Kisenosato's run might still have qualified him since he was born in the right place (depends on if his 13-11-11-13 gets him to Ozeki since as stated it doesn't, so the beginning of the long Yokozuna run merely gets him to Ozeki - but probably the long string of 10s followed by the above 48/4 would be enough), and Kakuryu would be up for promotion for the next 2 basho); Kotoshogiku, Goeido, and (for now) Takayasu don't quite make it to Ozeki. Hakuho, Harumafuji, Terunofuji and Tochinoshin would be the same. I think that's a totally fair way of slicing them given their accomplishments, just as much as what we have now. Still doesn't leave anywhere to promote Hakuho to, and there would only have been like 10 Yokozuna in the modern era (that's just a guess), but it means we leave out the weak Yokozuna who stumble into 2 Yusho as Ozeki and the crap sack Ozeki that last for only a few years and don't make any serious attempt at promotion under the current guidelines.
I mainly like it because it would make being Sekiwake mean something a lot more than it does now because we wouldn't have the times like a few years ago when we had 6 new Sekiwake in 3 basho, making it almost a joke as half the division (ok, not quite) was a former Sekiwake, because there were 7 top-rankers that we have to add 4 junior sanyaku to and there's no way to get them to KK particularly often with so many rikishi ranked above them. With Kotoshogiku and Goeido as almost permanent Sekiwake, occasionally rotating out, it would be impossible to luck your way in, and most of them would be forcing their way in with 11 at K or 12 at M1, although maybe they adjust the forced promotion numbers up a bit. We could even implement pseudo- rank protection for them in case of injuries because of the higher difficultly of reaching the rank: the furthest they could be demoted is Komusubi, and a 7-8 while not the last-ranked Sekiwake always has them stay on as a lower-ranked Sekiwake. Then we can do something similar for Komusubi - not drop them out of the joi, keep the highest ranked one if they go 7-8, and be willing to promote a 3rd or more when needed.
Not that they're ever going to take my advice, but it seems perfectly reasonable to me, and stops them from putting extremely mediocre rikishi as their promotional faces.