I know this isn't going to be a particularly popular opinion, but I will present my evidence and reasoning and allow you to make up your own minds after that.
In Smash 4 Yoshi is largely considered at a high tier character by most players, usually sitting in at least A tier in most tier lists. While he is certainly better than he has been in previous Smash games, but this doesn't magically make him high tier.
The belief that he is high tier is based around the number crunchers who have pulled out his frame data and other values like his air speed, and his ranking is centred around his potential from these numbers, rather than his actual results.
And the crux of the matter is, 8+ months into the game's release and we still don't see any meaningful tournament results from Yoshi, and it's not from a lack of players trying to make him work.
Let's look at tournament results. Mr. Doom's equal 7th place at Combo Breaker was the first time we saw a Yoshi make the top 16 in a major tournament. Just think about that for a moment - it took 6 months for a supposedly high tier character to crack the *TOP 16* in a major tournament. Considering we've seen characters like Pac-Man, Mario, Duck Hunt Duo, R.O.B., Ness, Greninja, Olimar and even Samus, Little Mac and Mii Brawler all make top 16's before this point, that says something. Even Donkey Kong and Palutena have been getting good results in customs tournaments. And of course, other "high tier" characters - Diddy, Sheik, Sonic, Rosalina, Captain Falcon, Zero Suit Samus, Luigi - consistently and reliably place well. Since that Combo Breaker result, we still haven't seen anything from Yoshi players - no Yoshis in the top 16 at CEO, no Yoshis in even the top 32 at Evo (and there were two Wii Fit Trainers in that Evo top 32). Yoshi can't even place reasonably highly in smaller weeklies like Xanadu and Shockwave.
If Yoshi is so high tier, why aren't more pro players using him? Why aren't we seeing the tournament placings that reflect his supposedly high tier?
Certainly at low levels, it can be easy to see why Yoshi can be perceived as strong. He's deceptively quick, has strong attacks, and has little end lag on many of his moves. But it seems these strengths can be overcome at high levels and his weaknesses are exposed much more easily. He definitely has many strengths, but he also has some pretty glaring weaknesses.
His biggest weakness, as I see it, and the one that I think is ultimately holding him back from being high tier, is his lack of kill setups. If you look at his moves on paper, he has plenty of kill options - forward smash, up smash, up air, forward air (spike), down b, possibly even back air or neutral air or the back hit of down smash if used near the blast zone. But, he's got no true combos into those kill moves at kill percentages - so the reality is, he actually has a VERY hard time killing. Let me elaborate.
His grab is terrible to start with...it's slow with massive end lag if it misses, and his pivot grab is actually even worse because he plays a silly little animation when his tongue goes back in his mouth. It has shorter range than other tether grabs and is the only tether grab in the game that can not be used as an additional attack and/or recovery option. Once he has you in a grab his throws are abysmal. Forward throw and back throw don't KO at any meaningful percent (between 250-300% from the edge without rage), and down throw and up throw don't true combo into anything even at 0% (if you manage to land anything after a down or up throw, your opponent didn't DI or air dodge properly). He's got no kill throw and no kill setups off his throws at any percentage. His most damaging throw does 7%; hardly worth it for the risk of a whiffed grab. His command grab is decent but the opponent can control the direction the egg goes, can control the speed they break out, and take half damage when inside it.
In reality there's little real reason to fear shielding against Yoshi...his down air is his scariest move in this regard but even this can be entirely shielded without the shield breaking, as can his down b, and both of them are extremely punishable on shield. In fact you don't even need to shield his down b half the time, because the move has absolutely no armour or priority on it so he can be hit out of it by pretty much any well timed up smash, up air or other move that hits above them. His side b is the same story - any move with knockback on it (so pretty much anything aside from Fox's lasers) will knock him out of the move, and the move itself is pretty bad. Most of the time you do this move, it'll be by accident when you intended to use a forward directed up b instead...not good when you end up rolling off the ledge, or when you are trying to recover. That segues into the next point of his recovery.
Yoshi's double jump *needs* armour on it due to the fact he has no real recovery move, but it needs to be noted that it has heavy armour, not super armour, so he can in fact still be knocked out of it by a strong enough attack (and can actually be footstooled out of it too). If he's caught off stage without his double jump, or if he's stuck under the stage, he's gone for.
It's also a falicy that most of his moves are safe on shield...the reality is, most of them aren't. Down b, fair, bair, dair, dash attack, fsmash, upsmash and dsmash are all unsafe on shield.
Lastly it's been proven that Yoshi's shield is activated and deactivated slower than everyone else's, due to the animation he plays of turning in to or out of an egg. This means he cannot shield on reaction quite as quickly as pretty much everyone else, and also only really has his neutral air as an out of shield option. His rolls are also close to the slowest in the game with massive end lag on them, and while it's true that rolls should be used sparingly, this still needs to be taken into account. He's just not as good at dodging stuff as other characters are.
Ultimately though it's his lack of kill setups that are hurting him the most. Yoshi works best if the opponent is approaching him, but if the opponent plays smart and doesn't directly approach him, he really struggles to bring them to him and get KO's. His eggs are a great move but are not a reliable tool to force the opponent to approach. Jab 1 to up smash is possibly his best KO option but even that isn't a true combo. He can try to bait air dodges by throwing eggs to follow up with an up or forward air but smart opponents won't air dodge. Fair into the stage to up air can work but can be teched. All of his smash attacks can also miss completely if the opponent is too close to him.
TL;DR
Right now, the evidence just isn't there to support the common belief that Yoshi is a high tier character. He has real issues actually obtaining KO's as he has almost no genuine kill setups, and his lack of tournament results supports this. You can throw out as many raw numbers as you want, saying he has awesome frame data and high air speed and so on, but in my opinion, we need to stop rating characters like Yoshi on purely potential based on these numbers, and start actually looking at how the package comes together as a whole and what results he's achieving. I'm not saying he doesn't have strengths...he most certainly does have plenty of strengths that make him worth playing, However, the fact remains that after 8+ months we're still not seeing any success at high level with Yoshi and there is no evidence to support his usually top-10 spot on the tier lists.