I don't see capital ship as pure support ship. Yes it is ture that they are huge, but a small frigate is just as much a target as the capital ships are. If you destory you enemys firgate, you reduce there firepower faster, while destorying there capital ship, removes there firepower and abilities.
It is also ture that some capital ship are support ship, but not all. 3 out of 5 capital ship, for any of the three factions, are in fact support ship. But the other 2 out of 5 are not. That not with out saying that there could be some improvments, to that capital ship system.
When you look at capital ships you must look at them, as I look at what the Vasari have over the other two factions. The Vasari, does not have the most powerful shields, the Advent have them. The Vasari do not have the hardened hulls, The TEC have little more are about equal armor to the Vasari, as well as more(and higher) armor upgrades. The Vasari also don't have the most hitpoints which makes armor, more important. In one post, a every thing to cost ratio, found that the Vasari HC was about equal to ever one else. So what do the Vasari have over everone else? They are more technology adavacne then the other two factions, and comes in the form of an extra abilitie, to most of there ship. There HC has two abilities, to ever one else one, as well as some ship have abilitie while other for the other factions have non(the Junsurak Sentienel comes to mind).
So when you look at the problem with out taking into account abilities, you get the result, that the VAsari, are weaker then the other to factions, not eqaul. But when you giht as them, or against them you find that they are just as real as powerful as the other two factions.
When I looked if putting resources into capital ship or lower class ship with out taking into account abilities, I came to the same answer as you guy. Capital ships are weak when stacked against the same use of resources in lower class ships. I even do leveled up my battleship to see, when they would be about equal to the same use of resources, in everthing, and found that the battleship need to be level 4.
But after some fight with rebal forces, in which a on paper out matched battleship won, I had to take a new look, at how I was looking at capital ship. I found that the Power Surge on my Kortul Devastator, were more powerful an abilitie then the Skarovas enforcers abilitie to Reintegration. This is do to the fact that increasing fire power and repairing shileds(which allows, for better use of shield mitigation) was more powerful then the abilitie to replace lost hitpoints.
So when you look at lower class vs capital ship class, you must take the special abilities into account.
Now I'm not saying, that your capital ship strategy and fleet strategy should not work together in any way, or to have a fleet of nothing but capital ship. There also abilities on the lower class that work very very well with the abilities of your capital ship.
Also note, form a supply point of view that even maxed out, capital ship only account for 2 out 5 of every supply point, and this is when you are not playing Vasari. So not having the lower class ship as part of your plan, is just power plaing.
If I was to fight a fight, in which as was out numbered 5 to 1 in supply point I would lose, even if I had those supply points, in capital ship. I found that this is one of the reasons that I lose, when I go for a captial ship rush too. But if you can get about equal in terms of supply point you can still stand you ground. The only problem I see, is that you are just making your capital ship strategy into your fleet strategy, which means, that you are overlooking 3 out of ever 5 supply points(more if you are playing Vasari).
A capital ship rush is just as powerful as a HC rush(may be a little more powerful) or a LRM spam. You just need a fleet strategy that use the Capital ship strategy as its core.