Aw man I always liked the challenge of Italy in HOI3. But the focus trees do they work properly? An issue I have with the older games is that once something happens that isn't supposed to happen the whole game kinda stops working.
The focus trees allow for somewhat more fluid gameplay, and give players small goals to pursue. They're essentially timed decisions on a roadmap that give you
almost free stuff. I say almost, because doing focuses costs 1 political power per day. However the usual 70 PP is a very small price to pay e.g. for 6 civilian factories, rather than constructing them yourself over the course of many months using your existing civilian factories to do it. The focuses are essentially a form of mana and aren't realistic, but this is the system they've gone for.
Also, in vanilla they don't allow for a historical timetable: all historical events tied to focuses happen on the wrong date and you can only do one focus at a time, so things like the historical German pre-war naval rearmament focus, you might find yourself not doing until well into the war, when all the other more useful focuses have been done.
Speaking of useful focuses, a lot of them are no-brainers, so much of the perceived freedom of choice of having a focus tree is nothing but an illusion, since you'll always want to grab certain focuses ASAP.
HOI3 Italy is only very slightly less powerful in that regard to HOI4 Italy. It is weaker in research than it is in HOI4, but it isn't a huge deal, it has more than enough. It is about as powerful as France in both games, if mobilisation difference and focus trees are accounted for.
It was weaker in every possible way in HoI3, though not as weak as IRL. I certainly don't recall Italy unlocking 1944 fighters with trivial cost in 1937-38 ('39-40 post-MtG research nerfs) and churning out thousands of them, or having the possibility to get Greece and Yugoslavia as pre-WW2 "freebies".