A review based on numbers incoming, skip if you care about theme or how 'cool' the card is. I am also not considering Deadpool in my review, who is a uniquely decent fit thanks to his design.
I feel a lot of people glamorize Symbiote Suit without giving it much thought. They see +1 to all stats, which seems amazing, +1 hand size, now that is epic! And then there is also +10 HP, which is double what most heroes start with, wohoooooo! Let's break it down.
The +1 card: perhaps the most notable effect of the suit is the extra card you draw each turn. But that extra encounter card more than compensates and turns your income into negative, not to mention increasing the chance that you manage to draw just the Advance to lose you the game. Say you are dealt an extra minion or an extra side scheme. That's 3-4 HP to deal with or ~3 threat, plus potentially negative 'when revealed' effects. The amount of resources that will cost you to deal with this extra encounter is no less than 2. You are already spending your extra card AND then another one to deal with the extra bad stuff coming your way from the hazard icon. That extra cost can easily reach 3 or even more, meaning you never get to enjoy the card 'for free'. On the very same round you draw your extra card you will be forced to draw an extra encounter, which is putting you at a loss. And don't even get me started on the Standard 2/Expert 2 nastiness you bring to the table with an extra encounter card. One extra turn. That's what you get when you play Symbiote Suit and then potentially lose to Ruination, Cruel Intentions, Dark Dealings, or Overwhelming Force. Now, obviously, I am being cheeky here, as I am certain the large majority of players do not even consider Standard 2 and Expert 2 when playing, but for most encounters more than half the encounter deck will, in fact, consist of cards that cost you 2 or more to deal with. There's also a difference between an encounter card from Rhino and an encounter card from Loki or Venom Goblin. However, I hold the opinion that casual encounters are not indicative of the game and should be disregarded when analyzing Symbiote Suit. If you can win against Rhino with the suit, you can easily win without it as well.
The +1 stat: it is nice, and there's synergy to be had there. Readying effects can make you use that more than once per round, but you really need to lean on it heavily to make it work. One extra stat is worth less than a resource, so you will need at least one ready effect per turn to offset the cost of the extra encounter card. I can see some hope in certain cases, but you really have to be pushing it and dancing between the twilight zone of having enough ready effects and a sustainable board state, and finding the window of opportunity to play the suit and not getting buried in bad stuff within 1-2 rounds.
The HP: mostly useless. It means you can probably sustain one or two more hits before needing to retreat to alter-ego, assuming you are not playing allies that already keep you safe. Then you recover ... and realize you are back to square one with your hero at 8 out of 20 HP. Efficient healing effects are super rare, meaning you cannot regain such a big amount of lost health. Even rarer are the cases where you will need to be at 20 instead of, say, 12-15 to feel safe. The game has solid alternatives to dmg soak in the form of allies or various ways to defend, making that much extra HP the most useless part of the suit.
Where does that leave Symbiote Suit? To me, it's forever in the 'win more' category of cards that you can play and win, but your win outcome is not really impacted by the card itself, and rather the game progress achieved before playing it. I am fairly certain you can make your games more difficult, or impossible even, by playing the suit as early as possible. The loss of tempo on the turn you play it and all subsequent turns will be notable. Heck, I can even issue a challenge to all who disagree. Go play the Sinister Motives campaign Venom Goblin scenario at 21 Reputation and then at 25 Reputation. Then consider which feels more difficult.
The alternatives: Nick Fury attacks/thwarts for 2, blocks an attack, and draws you 3 cards after you have paid 4 (5) for him. He gives you INSTANT similar benefits to what Symbiote Suit would give you over 2-3 turns without the downsides - 2 stats now, 3 cards now, one blocked attack from the villain now (which is arguably better than 10 hp). Avengers Mansion is super expensive, but quite flexible. You can grant the draw to a teammate that needs it more, and apart from the high cost, there are no downsides (well, if playing Expert 2, this card is the prime target for Overwhelming Force, but what can you do). For those needing a bit of extra fluff to feel safer against attacks, Endurance is a nice and cheap upgrade that grants you this.
Conclusion: Don't do Symbiotes, kids! At least not on high game difficulties.