Where do you think Charizard stands on the tier list
This is the short answer to what I'm about to say. Customs off, Charizard is a solid mid tier character that takes substantial player skill and knowledge to be played effectively at a higher level of play.
Do you see him being competitively viable
Yes.
Alright, before my fellow zards come at me with blazing pitchforks let me explain.
If a character is unviable, that means that that character has absolutely zero win conditions against a good portion of the cast, especially the top teirs.
Alternatively, an unviable character might have win conditions against most characters so long as the other player plays poorly, but if the other player players flawlessly or near-flawlessly, the unvaible character will have zero chance to win.
Alright, so is charizard unviable?
An easy way to tell is to look at his worst matchup. Does charizard have a win condition against zero suit if the zero suit plays flawlessly?
The answer is no...
IF THE ZERO SUIT PLAYER IS A FLIPPING PSYCHIC
Okay sure, Zero Suit samus has all the tools in the world to deal with zard, if she the zero suit is perfectly on point, she will give us a ton of trouble because her options simply beat ours. But no amount of flawless play will allow her to pick the perfect option every time. Zero suit is a 50/50 character. She puts you in situations where you have few options to avoid a follow up attack, but she still has to guess what you're going to in order to land the next hit. If the charizard player guesses correctly and manages to avoid the follow up, he'll (hopefully) be put in a position where he can gain some momentum against the Zero Suit player.
Zard only needs a few seconds to turn the entire match around. Once he has momentum, he only needs to hit you a few times to put you into K.O. percent. Once he gets Zero Suit there, she'll have to avoid making any slip ups, or she's dead.
Alright, so how can Charizard be viable?
Easy really. Play him like a
Heavy. Not like a
Speedster!
Speedster characters are all about outplaying the character in front of them. They're faster, safer, and they'll combo you into oblivion if you aren't at the top of your game. Charizard can't do that, which is why some people get frustrated with him and say he's bad. He isn't bad, they're just playing him wrong.
Heavies are all about outplaying the other player! People have habits. They aren't robots, so they will make mistakes. If they don't, mistakes can be forced. Heavies are all about getting a read on the other player and exploiting that player's weaknesses.
Look at charizard. Poor dragon hardly knows what a true combo is. He's got bthrow > fair and... yeah. That.
But Frame Traps. Oh boy. He's got plenty of those.
When you play charizard your goal is to get into the other person's head, because that's where charizard gets most of his follow ups. If you land a B Throw > Fair, don't just stop there. Ask yourself, is the other player aggressive or defensive. If they're aggressive, Fast Fall after the Fair and wait for them to attack your shield. Then grab them again and get off yet another Bthrow combo. If they enemy is aggressive they're probably still trying to find some way to retaliate against you, so punsih that with a dash attack, unless they DI or jump away to safety, that's going to land and pop them into the air again. Now you just did 53% to them, and you have stage control.
Things like that are what charizard is about. Find out what kind of player the opponent is and try to exploit that. Advantages are harder to gain, so make the most of them! Most importantly, be willing to mix up your playstyle to suit both the player, and the character they choose.
(On the defensive end, knowing if your enemy is the type of player to rush directly at you, or bait out an option then punish will help you to escape combo strings and juggles.)
Do you think charizard can handle his bad matchups enough to stand a chance at winning?
Hyup. Remember that ZSS example I gave? You just have to apply something similar to every matchup. Charizard has options that let him punish players extremely hard once he catches on to whatever patterns they have. So find out what kind of player the opponent is, and use that along with whatever matchup knowlege you have to outplay the other guy and win.
Charizard doesn't have any unwinnable matchups... just hard ones.
tl;dr
Charizard is viable. He just takes work.
Unless customs are on, then spam Dragon Rush all day. That move is dum :/