I still believe that removing any unit cap is a reasonable solution to the problem.
You have valid points, but three of the main problems I can see with removing the fleet point system are:
1) It would de-value capital ships fairly considerably. Of course, there are people on both sides of the fence on this, some would love to see more capitals and some are happy with the way it is. But essentially, right now the number of capitals is balanced mostly by the fleet point cost and research. In small-medium sized games, the fleet point cost is a much bigger concern than the research. This forces the player to diversify the fleets somewhat, and have capitals mixed in with frigates and support cruisers. With the economy in its current state and the ability to hoard resources infinitely, removing the fleet point cost would allow a player to put out considerably more capital ships and greatly reduce the value of each one while at the same time reducing the need for fleet diversity. Why build light carriers when you can just get 5 Sovas and get 15 squadrons out of them right away (training to level 3 with credits), as well as their other abilities. Why build cobalts when you can build a bunch of Kols that can cover a much larger area with weapon fire and have improved shield resistances..
Research would still limit how many capitals you can have out, but in small/medium games I would expect to see a heavily disproportionate number of capitals vs support ships. Again, some may like this, but I think the current way is better.
2) It would also devalue expansion somewhat. Same as the above, there are people on both sides of the fence on this one. The main main problem here is that Volcanics specifically provide greater fleet points, which makes them desirable contention points, as well as desirable strike targets as losing a fully developed volcanic can really set a player back on military production. You would still need to expand your empire for logistics and setting up the economy, but the fleet point system right now plays a large role in it, also.
3) And this is probably the main one. Currently, the Vasari are mostly balanced by their higher need of fleet points, in the late game. With resource hoarding and rates of increase in large games, the difference in building costs between Vasari and TEC ships becomes pretty neglible--it's the fleet points that limit Vasari military production and maintain balance between the ship-to-ship weakness of TEC ships vs the Vasari ships and the greater maximum number of TEC ships vs Vasari ships. Taking away the fleet point system would allow the Vasari player to potentially produce the same number of units as the TEC player, and each of them would be individually stronger. It would take quite a fair bit of rebalancing to straighten that out, and the Advent is in the mix also though we beta testers don't know how