+1 Action and +$2 (which is worse than Silver since it can be drawn dead)
There are threads on this forum about the difference between Ducat and Candlestick Maker which show why the opposite is true. Action Silver is most definitely better than Silver. If Patron did not exist, Action Silver would be a $4.
How so? Throne Room variants and Storyteller are too fringe-case to really say that Actions are better than Treasures because of those combos. (And even if Action Silver is between $3 and $4 worthy, that still doesn't change Vanguard being generally worse than Laboratory.)
TR variants (7), draw-to-X (5 cards), Actions that want Actions in your deck like Ghost, Golem, Herald, Vassal and Scrying are 17 Kingdom (yeah, Ghost is not but you can gain it two different ways) cards. That does not constitute a fringe case. Not to mention that sideway cards like Academy, Piazza, Innovation, Citadel also like Actions. Among the Landmarks we have 4 that like Actions (Colonnade, Obelisk, Orchard, Triumphal Arch) and one that likes Treasures (Keep).
Again, just read the threads about Candlestick Maker vs. Ducat. If your argument were true, Ducat would be better than Candlestick Maker in two respects (on-gain ability plus Treasure>Action). But in fact, a Coin yielding non-terminal Action is on average preferable to the Treasure equivalent which is why Ducat is a fine design, its on-gain bonus is compensated via being weaker on play than Candlestick Maker.
Are you missing the fact that Vanguard gives +$2 when you've drawn your deck and a Lab would do nothing? I know Vanguard can get messed up by mid turn reshuffles but that shouldn't happen too often if you play carefully - and if you're drawing your deck every turn that just won't really happen. It seems better than lab generally to me (not strictly better).
Not being able to triggle reshuffles could be a serious liability but I tend to agree with you. The card is overall similar to Minion which also does two things, drawing and providing Coins.
Even without discard for benefit you do often enough want to overdraw (e.g. because you intend to green soon and then your engine must be able to handle the extra cards) and Vanguard reduces the opportunity cost (you could have gotten payload instead of draw power into your deck instead) of overdrawing.