Oleg, the 6.5 Carcano had a few "issues".
The Italians used gain-twist rifling on a good portion of their 6.5 Carcano issue guns. As long as the final rifling twist was matched to the bullet weight and length, all was good. Sporterized Carcanos often had several inches of their barrels cut off, and those were crucial inches with respect to that gain-twist rifling. So the guns, understandably, shot poorly after being brought home in duffle bags and carried afield in search of venison and the occasional U.S. president. While it's use as a varmint round for the latter is now a matter of record, it didn't endear itself as a popular sporting caliber otherwise.
The 6.5 Carcano also showed up, as issued, with a slightly oversized bore, instead of being .264", it often ran as large as .268 - .270". Call it poor QC, call it being unique for the sake of being unique, but folks shooting .264" bullets weren't getting good accuracy out of their Carcano rifles. BTW, there's a company called Mo-Loc, who make oversized .268" bullets specifically for these rifles.
Somebody in the annals of gunrag history let it be known that the Carcano action, particularly the striker retention mechanism, was poorly designed and an accident waiting to happen, potentially driving the striker into the shooter's face at the wrong moment. This in spite of the fact that the Carcano was derived from the Mannlicher turnbolt action, even the 6.5x52 Carcano cartridge was a kissing cousin to the famous 6.5x54 Mannlicher-Schonauer round as supposedly carried by Karamojo Bell. This reputation as a handgrenade-in-waiting didn't help the gun and cartridge in popularity, either.
As an aside, a friend bought a $39.95 Carcano from Springfield Sporters, chambered in 8x57 Mauser, a last-ditch Carcano from WWII. I loaded up some 170gr blue-pill proof loads, using lots of pistol powder, for the experiment.
Once we followed the trigger string back to the remains of the rifle, it was obvious the striker assembly had stayed right where it was supposed to, inside the bolt, right where it was before the proof load. The bolt, on the other hand, had come aft a wee bit - because the forward receiver ring had shattered.
The 6.5x52 Carcano is actually a quite decent and efficient round, not too different from the 6.5x54 Mannlicher Carcano. It does have an odd case head size for most bolt-action rifles, although it's close enough to the 7.62x39's case head size to be useful for custom bolt guns based on the latter. The 6.5x52 Carcano, 6.5x50 Arisaka, 6.5x53R Dutch Mannlicher, and 6.5x54 Mannlicher-Schonauer simply suffer from obscurity, and some measure of notoriety.