Why don't we see more rifles in 7.62x54R?
Why don't you see new rifles in 8mm Lebel, 7.7mmJap, .303 British, or any of a dozen or more obsolete military rounds?
because there is no market in the USA. These old milsurp cartridges (and I do have a collection of rifles for them) are 1) not as efficient as sporting rounds as newer "mainstream" rounds, 2) odd or unusual dimensions, and 3) a niche market, at best.
In the case of the 7.62x54R, while ammo was commercially produced for this caliber since the early part of the 1900s, it has always been made only in very small amounts. No significant market.
Some here will have a hard time believing it, but there was a time in the US (close to half a century after WWII) when rifles (and their ammo) for ANY of the COMBLOC calibers was really scarce. Guys that brought back SKSs and Moisins from Viet Nam usually hung them on the wall, because 7.62x39 and 7.62x54R ammo was virtually non-existant in the US.
With the collapse of the East Bloc, and their subsequent dumping on the US market of any kind of gun and ammo that we legally allowed, its common today. But it didn't use to be that way. So, no historical market in the past.
And even today, finding good quality hunting grade ammo for the 54R (especially in reloadable brass) isn't simple, or easy.
it won't fit in an AR, even an AR 10 class rifle, because of the rim diameter, and the feeding issues from the rimmed, heavily tapered case. You could build an AR style rifle to fit the round, but it would nearly all have to be made from scratch, other than the furniture, and maybe even that.
And even if you did, who's going to buy them when the .308 is already there to be had? Any of our common sporting bolt actions could also be adapted to the round, but again, there is no market. The time, effort and money needed to make them would be mostly wasted. Outside of a few collectors and enthusiasts, there just isn't anyone interested.
The milsurp market is the only reason its a popular round today, and the guys who buy cheap milsurps aren't a good customer base for mass market sales of new sporting rifles in milsurp calibers. They already have milsurp rifles for their shooting needs. And the sporting market isn't interested, having a plethora of rounds that perform better in the game fields already.