It's the LRM. Sorry. Quite frankly, no one complained about capital spam, or heavy cruisier spam, or carrier spam.
This is a symptom of appearance. Every race gets the T2 LRM analogue relatively early in the game, and while they differ cosmetically, they perform the same function. They are cheap, and hence we get the appearance of 'spamming' because the strategy is very possible with every race with a good economy.
It's really a problem concerning the effectiveness of T2 ships. Games tend to get 'decided' when Tier 2 rolls around with LRMs. Their effective counters are generally more expensive, and frankly, not very effective against anything else. Flaks and fighters generally counter LRMs and bombers, which is kind of strange, but makes sense if you think of LRMs as some kind of 'frigate bomber.'
The misconception also comes through as LRMs are also effective against 4 main types of targets, defenses, structures, workhorse frigates and Capital ships.
Games for some reason, tend to be decided in the tier 2 phase when TEC enters primality- traderoutes are getting setup, neutral planets have been taken. Advent and Vasari need to 'react' to this tradepost dominance. They don't actually have anything that gives them a 'boost' to defeat this early economic superiority; their ships are not better early game, and they have no substantial late game abilities that might allow them to overcome the 'hump' when the midgame rolls around. (Vasari does have the ultimate endgame ability, but quite frankly it doesn't matter in these situations).
I think it is rather strange, that LRMs are overall cheaper and easier to mass than workhorse frigates. While they do cost crystal, it is only a small amount. This effectively makes them also good against utility frigates, like Hoshikos, Guardians, Subverters, etc, in the same manner as workhorse frigates, being that they are too numerous to affect.
(They of course don't have special ability-use hosing abilities)
I think perhaps the solution is to make utility frigates cheaper, or easier to access. They aren't terribly effective against 'the big 4' (Structures, caps, defenses) and they aren't effective against workhorse frigates. Cheaper utility frigates would be able to sway battles more in favor of the Anti-LRM, and they'd increase the combined armed nature of the game, as massing utility frigates doesn't make a terribly great amount of sense (except for perhaps guardians). Utility frigates are also unique to each race- in game design terms it would help with differentiating the players by making combat 'different' rather than a simple mash up of Light+LRM vs Light+LRM
Vasari Subverters are Tier 5. I think the game would be well served if Subverters were brought down the tech tree to tier 3, and perhaps if Advent's culture bonuses offered a more substantial 'homefield' advantage in the early game, perhaps by quickly increasing the loyalty of local planets for tax revenue, or perhaps if they had a cheaper cost (Crystal.)