The whole better rifle cartridge is something of a red herring when looking at the Italian WW1 experience. Long range shooting just did not happen with a rifle.
It didn't happen with most/all WW I armies.
The problem was with the ammo selections of the different nations. The 'firepower' of the infantry had shifted from
the rifle to
the machine gun during WW I. But the standard of MG issue per battalion and shifted from 2-4 machine guns per battalion to a dozen or more guns per battalion and in 1918 may armies were issuing Lewis guns, Chauchat', BARs and cut down Maxim guns in addition to the Battalion machineguns.
In fact it had shifted so much that the US, British and Germans all came up with special long ranged ammo for the tripod mounted machine guns that allowed for long range fires (like over 1800-2000 meters) and the French 1890 balle D already allowed for long range fire.
The US shows some the choices in ammo and how it affects things.
The US adopts the 1903 rifle and cartridge (basically a more powerful 30-40 Krag)with a round nose 220 grain bullet at 2300fps. Within months the US realized they had screwed up and came up with 30-06 (slightly shorter neck) that would allow for a 150 grain flat based spitzer to be fired at 2700fps. The existing rifles could have the existing barrels taken off, shortened a bit and rechambered for the 2mm shorter cartridge with the proper gap between bullet and rifling for good accuracy. Also needed some new sight part/s. All was good until 1916/17 when the US figured out that the exiting 150 grain/2700fps load, while good for long range rifle shooting (600-800yds) was seriously lacking for long range machinegun fire. That 1800-3000yd barrage fire well loved by WW I machinegun theory.
The US leapt into action and came up with the M1 30-06 load with a 172 grain spitzer boat tail bullet at just under 2700fps which added about 2000 to the max range. However max range called for a lot of elevation and most/all bullets started tumbling well before reaching max range. Effective range could be around 2000 yds less than max range. This was in 1917/18.
US manufactures millions of rounds of both kinds of 30-06 ammo in 1918-1919 (production took a while to stop) which had several effects in the early 30s.
1 was that the US decided they had too much ammo in storage to change over to the .275 Pederson round for a new semi auto rifle.
2. US policy was to use the oldest ammo first for training. Which meant that the 1917 M1 load with the boat tail bullets didn't show up on training ranges until the mid 30s at which point they discovered it was so long range that it was unsafe on many existing ranges, which lead to the M2 ball 30-06 ammo which was the old 1906 load updated with new powder.
The new load operated at lower pressures than the old and didn't put as much wear and tear on the M1 rifles but any 30-06 gun could fire any 30-06 ammo although sight settings may be off.
The US did try to issue the 172grain BT Spitzer to the Browning belt fed machine guns where they could (some what easier as the Brownings were feed by belts).
Yes the M1 rifle and the Bar were a bit over powered for squad weapons. But the US was trapped into the 30-06 cartridge (mostly) for weapons development and didn't break out until the M-16. The 7.62x 51 was not even a 30-06 junior. It was the old 1906//1930s M2 load in a short case allowed by new powder development. Some armies were more than stupid when it comes to weapons development.
Yes a large side track. But the Italian 7.35 saga is rather sad. Use a shorter, fatter, lighter bullet with a better point but don't fire it than much faster. Try to use it in both rifles and the platoon LMGs, which means you
NEED a larger more powerful round in the the company/battalion/AFV machine guns complicating the logistics.
Now the Italians get caught by the terrain they are fighting in. Instead of mountains, cities and forests like many other nations (and Italian planning?) they wind up doing most of the fighting in North Africa with some of the most wide open terrain of WW II. Most (all?) countries did not need the complicated sights used by the Americans but using a fixed distance on the main battle rifle is a mistake. May simplify training but it your average soldier can't hit well on the training range he isn't going to risk firing at long range (long being much beyond training range). You spend a lot of money on a good bolt action rifle and powerful ammo (compared to a 9mm submachine gun) and then save a few lira on the back sight?
At least the British gave the soldiers the illusion they could shoot back at long range
It turns out that according to one study that about 50% of rifle fire was done at 200yds/meters but that means that 50% was done at over 200 yds/meters. 98% was done at 400yds/meters or less. Yes really long range was rarity. But abandoning the 300-400yd/meter range band might not have been smart.
Same study said that 50% of machinegun fire was at 400 yds/meters or over. If you want a common cartridge for both roles which side to you favor/lean towards?
Now a problem for the Italians is they don't have enough LMGs per platoon/company to equal the British number of LMGs per platoon company at 200yds and beyond and the Italian rifles don't have the sights or ammo to try to fill in even if the officers can get them to shoot (same for the British, getting the troops to shoot at the longer ranges was always difficult.)
The Italians need to figure out where they are going to be fighting, what weapons are going to work where, how much training they are going to pay for.
If you want a gun that uses a single sight setting for ease of training then buy gun/cartridge combo that gives a flat trajectory out to 300-400meters.
Italians tried to build a gun that used a single sight setting and then due to circumstances paired with a cartridge that gave a rather curved trajectory.