I feel Grittle is separating it into the engineers who are the new recruits and the crack veteran squads who fought on the Eastern Front who are in short supply. Then you have the regulars through doctrines.
You got most of it
The main "flaw" of this faction is the lack of a non-doctrinal backbone generalist infantry like reefermen or grenadiers.
Sure, Guastatori looks like the mainline infantry. but they are a 4 man Engineer Support squad of sub-par volks with sub-par rifles whose main role is to support the many vehicles of the HGK. Heck, in order to make them as close to mainline infantry (Get AT snare, extra man, LMG rack that all your infantry can use.) as possible requires a pretty pricey upgrade of 250 manpower, 40 fuel. that could have been easily spent on a Marder or L6 Light Tank.
The Bersagleiri is the Elite Infantry of the army, basically there to prevent a problem with the USF for awhile with just blobs of Reefermen and lack of infantry variety. the Bersas provides a small yet potentially surprising/useful infantry that can support the light vehicles by instead of repairs and capping, but dealing with any AT infantry or Tank snares that could hinder the vehicle advance.
Even then, you can easily skip the Bersas, who are unlocked with T3, by just going T1 and T2 and rushing T4 for P4Hs and the glorious Berge
But if your too diaper baby to play this faction without you beloved reefermen or grenadiers. there are a nice selection of doctrinal infantry you can use to ease your way into the faction:
Alpini Brigade is the closest you get to backbone infantry, being in 2 doctrines (Italian Remnant, Mountain Warfare) really helps with the variety. They come in alittle late in the early game at 2CP. but they can use volley fire, ignore speed penalties in rough terrain (they are mountain troops), have access to basic grenades, and come in a 5 man squad. However, they lack AT, and don't have access to panzerfausts, and are fairly pricey at 290 manpower.
Panzerjaegers,on the other hand, are AT specialist, they are a fragile 3 man squad that carries 3 panzershrecks that they can holster for their weak rifles, and has the ability to fire 3 panzerfausts (1 per squad member). They cost more at 370 manpower, come in at 4CP, and the panzershrecks they use are much more inaccurate and deals less damage than a regular shreck. so they have to go close to the enemy tank to dish out effective damage.
You have the small weapon crews (Brixia Mortar and Breda 37 HMG) that you usually wouldn't have. nothing really special about them except the Mortar has a fast firing rate and that they both can retreat without the Defense Vet 2 bonus, so you can go full offense on them.
Then your Have San Marco Marines, infiltration specialist, that poop out of buildings and do sneaky stuff, like plant demo charges and other explosives behind enemy lines and duke it out close range with FNAB43 SMGs. they camo and the doctrine they come in also has a separate pricey late-game ability where you can sneaky sneaky them via plane and parachute pre-vetted behind enemy lines.
Italian Militia poop out of the Forward Outposts in the Italian Infiltration Doctrine. they cheap, fragile. basically soviet partisans that use rifles and has no camo. they can also plant explosives. but that's about it.