Slightly related to the OP's idea of the game's largest 'structural flaw', in my opinion there are three 'big' (yes, this term is relative) flaws with the game:
1). Level of variance, particularly with terminal actions (essentially the OP's argument) but also with specific cards. For example, opening Sea Hag + Masquerade.. both good cards, and with good shuffle luck *very* good.. but quite poor if you, for example, draw the Sea Hag with the Masquerade. I don't know if anyone here has played a lot of fantasy RPG games (anything based off of Dungeons & Dragons), but over the decades of digital versions of these games, the concept of a 'critical hit' has been the classic example of the problems of high variance events. For those not familiar with the concept, typically every attack has a small (often 5%) chance of dealing double damage. This variance, both in frequency and power, has the effect of trivializing encounters when the player gets 'lucky', and causing balance issues when they don't.. the problem being predictability. The more rarely critical hits happen, the greater the impact they have in those rare fights where they actually happen. The solution? Well, D&D 4th edition chose one of the two routes: weaken the effect of critical hits. Critical hits in 4e only deal maximum rolled damage, instead of double rolled damage. The other option, chosen in games like World of Warcraft, is to increase the probability of the critical hit event. If, for example, critical hits happen roughly 40-50% of the time, they can be relied upon to happen numerous times each fight, and thus can be correctly balanced for. For a game like Dominion, however, realistically adjusting variance of action collision (as well as dead actions) would totally remake the game.. plus simply weakening the impact of action collision by making actions overall weaker sounds like a bad plan.
2). Single cards and 2-card combos that are optimal in exclusion of anything else. I'm talking here about 'combos' like Minion + more Minions.. or Hunting Party + $2 action + more Hunting Parties.. or Fool's Gold + more Fool's Golds.. or Bridges + Native Villages.. or Chancellors + 4x Stashes.. or any number of specific 1-2 card 'combos' that really can't be improved upon by adding any other (action) card to the deck.. or sometimes any other card at all. Cards like these really defeat the function of a 10-card Kingdom.
3). First-turn advantage. For a high-quality competitive game, a first-turn advantage of the scale that exists in Dominion seems to defeat the function of the game from a purely competitive standpoint. What I'm getting at here is that all games fall somewhere along an axis of luck vs. skill.. 'casual' games typically fall closer to the 'luck' end, while 'competitive' games typically fall closer to the 'skill' end. In my opinion, for the depth and complexity of discussions and the playerbase of Dominion, the game is surprisingly higher on the 'luck' side than most other purely 'competitive' games.