Too few little bits won't help enough. As I've said, the game has a clock; your own HP will run out in an average of 6-9 rounds, so you're not usually able to win unless you can do it in that amount of time. You need to aim for around 9 damage per round against Dawn, for instance; you won't do 9 in the first round, of course, you'll make up for it toward the end, but every turn in which each hero is only worth 1 or 2 damage is a round where you're not pulling adequate weight toward the goal. This is particularly true with 3 heroes, since no villain yet created has [H]-based HP (though the Dreamer comes close, as do the Vengeance Five and the Ennead - perhaps for accuracy's sake I should say no single villain target has HP which varies this way).
~ Being irreducible doesn't matter…except when it does, like every other effect in the game. Very few abilities are useful all the time , otherwise what would be the point in having different abilities/decks/scenarios?~
Except against Miss Information, Lightning Slash is pretty much always good. So is a card that draws you cards (and yes, Recompile does that, but not without cost). Again, my tolerance for highly specialized weapons is greater if they are tutorable singletons; if they clog up your normal draws and get in the way when you don't need them, they're just landmines in your deck that show up now and again to give you a bad game, and that's not cool.
Also, with the max discard from Recompile you get back six cards. Six! Can anyone else draw that many at once? The only person I can think of who can manage it would be Fanatic when her only available card is Prayer of Desparation.
You have to pay four cards to draw those six, so it's only a profit of two cards besides itself. AZ, Bunker and Tempest can all match that (though only Tempest doesn't expend his Power for the turn doing so); Scholar and with a bit of jiggering Fanatic both far exceed it, though at the cost of the rest of their turn, unless they get an OOT play.
Oh, Voss, do you have soak with all those minions? Well, Legacy is gonna give you one hell of a punch in the face right now 
If it's a 90-damage punch, great. Otherwise, those villain targets you've been leaving in play will probably just overrun the earth. Personally, I see no reason to let Voss keep his bodyguards for any length of time.
You probably need to stop looking at these decks/cards individually. Yes, some stuff is utterly useless some of the time, but other times that same useless stuff becomes absolutely epic.
And again, search cards are the way to make that a viable strategy (though even so you occasionally get boned by the random draw, having Fanatic start with Wrathful Retribution for instance). Or even better, modular cards - ones which have a wide variety of different uses, one of which is likely to fit the situation. As it stands, I am forced to evaluate every card according to how often it'll do useful things (alongside how cool it is, but that's a far lower-order criterion, more of a tiebreaker than an actual factor), and if that's too low compared to how often I'm going to see it in a game, that card is a bad card. And a deck with too many bad cards is a bad deck. Legacy is a hero with a bad deck (some good cards, yes, but not enough of them), who is not a bad hero only because he has an absurdly good Power. Visionary is a hero with a lot of bad cards, but I'm not sure I'd say she has a bad deck, since she has several insanely good cards and has her innate Enlighten power to accelerate and filter her draws, so cards like Brain Burn and Mass Lev are a fairly manageable inconvenience (unless you have Setback's own luck on the draw, as I seem to).
In that context, Parse strikes me as an experiment in design - building a hero with a LOT of highly situational cards, and then giving her tools to sift through them in search of the ones she'll need. It's a neat concept, but so far I haven't seen much evidence that it performs up to spec. Again, future plays may convince me, as they largely have with Mr. Fixer, but it's not certain.
that's the kind of stuff the game is all about. It's a team game, a co-operative game - it's not about "my deck is better/worse than your deck", it's about "hey cool, if you do that thing and I do this thing, then that really cool thing happens and we both feel really good about it".
Those moments are certainly nice to have, but I'm a bread and butter kind of guy, I don't care how good the food at Le Cordon Bleu is if I can only afford to eat there once a year, because I have to survive on something else the rest of the time, and I'd rather make sure the something else is good enough for me. So my ideal hero is one where EVERY card in his deck is good, even if none of them are great. I think the overall closest one is Tempest; other than duplicate Limiteds, about the only card in his deck I'm not thrilled to see is Elemental Subwave Inducer, and maybe Grevious Hail Storm but even that one is at least handy. That doesn't mean Tempest is my overall favorite hero, but he is pretty much what I'd regard as the Gold Standard of quality, or pretty close to it. I don't expect everyone to measure up to his level, but they have to offer something else comparably desireable, such as the extreme risk/reward equation of Absolute Zero, or the control trip you can get playing Visionary. That last might be the best bet for me to eventually appreciate Parse, but once again, I haven't seen it happen in the three games I played (perhaps because two were against the Vengeance Five, I'm definitely done with that matchup).
I know you say stuff like "Oh, but the chances of that situation coming up are so low…", but well, that's half the fun - that one time you manage to pull off that epic thing out of nowhere, and it still gets mentioned months later because all the players gleefully remember how cool it was. That's why I reckon this game is so cool - it has so many possibilities, random variables and stuff that can happen as a one-off uber combo (or whatever), and you get to sit down with a bunch of people and all enjoy the uberness, and then play it again and maybe some different uberness will happen. Or you get utterly flattened and instead can talk about "omg remember when we got wiped by X in three rounds?", and then plot revenge against them and come back and kick their arses :D.
Eh, kinda. I do like the way SOTM really gives me a sense of alternate timelines and shifting destinies - the way targeting is based on current HP totals (other than Lowest HP, since that never changes itself) means that just deflecting a single attack can change the outcome of the game. So that immense variety and replayability is a definite strength - but it doesn't stop me from feeling cruddy when I draw yet another opening hand along the lines of 2x Brain Burn, 1x Mass Levitation and 1x Mind Spike. Above all, I always live in the present moment, and so what I want is always a hero who is confident that he has the card he needs RIGHT NOW, just at his fingertips. CR is perfect for this, Ra is pretty good, the Wraith is almost too good - there are a lot of heroes which can do this. If Parse can't, she may well just not be the hero for me; I'll still play her an equal share of the time, but perhaps mostly in solo games. (It's probably not a coincidence that the hero I enjoy most, Nightmist, has been played in real games a full fourth of the time, whereas my overall ratio of solo games to non-solos is more than 2 to 1.)