My thoughts:
Having middle vp matters a lot actually, it gives you a lot of extra sight. You know what is in the central vp building. Is there an mg in there? No? Get one of your own in there and you get great control. Yes? How to flank it then?
You know your opponent has a lot in the middle? Attack his fuel, and send one squad to the 3 points on the west. Opponent will focus the attack on his fuel, get some of his troops there but probably won't care too much about the points on the left. If he does get a squad there, then you can send a squad through the middle to flank the mg in the building and get it out.
If your opponent has a lot on the right side and on the left side, just go to his cutoff through the middle. This way he wont get resources from the right and he will have to rotate which gives you the opportunity to easily get his fuel. From the mid you can also easily get cutoffs on the left in case he got a hold of your fuel.
Hope this helps a bit, really depends on the situation tbh tho, but attacking cutoffs is often better than directly attacking an opponents fuel.
I understand what you say but I'm only talking about the best value you can get from those scenarios, much more what OrangePest is talking about.
Center VP being excluded is a matter to reduce the number of scenarios, of course center VP matters on a game and having it or not may change your strategy.
You're a much better player than me but I disagree that cutoff matter more than the fuel point itself. I'll say this is true in COH but not so much in COH2. Of course cutting your opponent is valuable but not always as much as we think during the game. There are a lot of parameters around it, but I'll say that in general if you can't cutoff your opponent for more than a minute and can't decap his other points, the value isn't so important.
Personally I've been disappointed various times by harassing my opponent fuel on Crossroad (and this is why I open this topic), taking it and the middle point connecting it to my side weren't enough to take the fuel lead. I've been reviewing my replays and see that at the end I was only able to gain 2 or 3 fuel more per minutes than my opponent, also because of course he is also active and harassing me. But even in the case of keeping my fuel and disconnecting his fuel, I had the feeling that the value wasn't enough for the investment.
So lately, I decided to change my strategy and focus more on the 3 points facing my fuel, trying to always being active at capping it and saw from it better results in term of fuel advantage.
The CONS for this strategy is the VP control since usually when you manage to push off your opponent from his own fuel you're also able to cap the VP next to it.
But that's just my perception and I'm interested to read others.