The progressive (gain) twist rifling used in the Carcano barrel was intended to give higher velocities at lower pressures. The 160 grain 6.5 bullet was standard fare in virtually all the early 6.5 cartridges and none of the others saw any need to use a gain twist. There was no real benefit to it.
The real reasons for the Carcanos lack of popularity are numerous and I'll try to hit on a few of them.
The cocking cam was steep and cocking effort was relatively high.
The forward placement of the bolt handle was awkward in use.
The split bridge made necessary by the forward handle placement also made scope mounting problematic.
Clips were necessary for the magazine to function. In addition, the action was suitable for the Carcano cartridges only. (actually, a friend of mine converted one to 35 Remington and it worked reasonably well).
The safety was awkward to use and not in any way convenient.
The overall quality of workmanship was crude.
The Japanese used a rifle, made for them by Italy, which was a Carcano with a Mauser-type magazine. Called the Type I, this rifle was chambered for the 6.5 Japanese cartridge. I had one of these which was quite accurate but still crude. GD