My idea involves bringing the bullet diameter up to 6mm - purely due to the fins.
This gives a massive boost in energy
There's more to it than mere diameter..
The projectile needs
some sort of ballistic coefficient for when it leaves the barrel. Or, we'd just have long rods in the cases.
Adding fins to conventional projectiles has not proven to be of much success, when tried.
Part of that is in the fact that from the average firearm a projectile emerges at around 30,000 RPM, so, fins are of little use, and could be said to be counter-productive.
Now, in tank munitions, there are a number of other considerations at play. One is that, for kinetic armor penetration, there's a length-to-width ration that runs from 1:16 to 1:19, with 1:17 about ideal. For tank killing, rather huge velocity is also wanted. Whic his why most tank cannon are around 120mm bore, and use discarding sabots to support the sub-caliber projectile (which is in the 60-70mm diameter range). The circa 4000 fps that generates facilitates hitting targets at range expediently.
Now, people tinker around with all sorts of things. Like necking a 280 cartridge down to 6mm or even 5.56mm, but the results don't generally do anything better than existing combinations do.
Witness the 6mmArc, in many ways, that's an "optimized" 5.56 round. A 60-70gr round at near 3000fps. But, it's not that much better than 63gr 5.56, so "adoption" has not been overwhelming.
There's probably an "ideal" rifle round lurking out around 7x45 or so. But, there are so many 6.8mm rounds that already exist, and 270 and 280 as well, in case dimensions from 40 to 56mm long as to have pretty much trod all the ground there is for 7mm.
The Xcellerator rounds were interesting--poke a 55gr 5.56 round into a sabot and plant that in a 30-06 or 308 case, These whistled out around 3200-3300fps. Typically they'd print high & right by 6-7 inches, versus their full-bore counterparts. The question of why would a person want AR performance out of a Garand or M-14 becomes a legitimate question to ask.