My opinion changed a lot on Yoshi when I read someone say that he was a character designed solely on making advantageous trades with his high damage, fast moves. If the Yoshi player aims to make as many trades as possible throughout the match, then eventually the Yoshi player will be in the lead and the other player will be left wondering what happened.
This is why early on some people thought Yoshi beat Sheik or at least went even. Later on opinion changed, but I wonder if people don't underestimate that aspect of Yoshi. He doesn't necessarily center around playing a traditional neutral and winning, more around making trades, but that's not to say he has a poor neutral.
His moves don't, "flow," particularly well, but I sort of doubt how much this really matters. He seems like he relies on hit and run strategies and a great disadvantage state more than anything. The, "hit," is just a strong damaging hit, potentially through a trade, and the, "run," is more of a lack of followups off of the hit because that's the nature of Yoshi's moveset. But when Yoshi lands a hit, I don't know that he necessarily needs followups, considering the damage on his moves and the fact that his moves knock the opponent away so that they won't immediately threaten him again.
It's not easy for the opponent to chase Yoshi. With his mobility and decent anti approach moves like eggs and pivot neutral b, or situationally fair, the opponent can't just pin him down in neutral. His perfect pivot and options out of perfect pivot are pretty great too.
It's definitely not easy to capitalize on Yoshi once the opponent is in, either. All it takes is one mistimed combo move for the Yoshi to respond with 10 damage and a neutral reset (nair), or for the Yoshi to use jab and turn the tide really fast, especially if they get jab usmash. The nair combined with frame one heavy armor and low fall speed make Yoshi arguably one of the hardest characters to combo. As for edge guarding, I think Yoshi's recovery is more than ample. Especially for horizontal recoveries, I almost never see Yoshi players get gimped. His air speed, up b momentum changing, and command grab make it pretty challenging to juggle, and originally I wasn't going to mention it, but since I've seen it kill a few players in tournament, his down b has to at least be watched out for when trying to juggle him. And since he's heavy, he won't die till late, especially compared to some of the top tiers.
I think it's pretty important to emphasize how much Yoshi can capitalize off of reads as well. His uair combined with jump height make air dodge reads scary, a roll read can end with 32 damage off dair, etc, and he has the mobility to make it work.
I still think Yoshi is a high potential, underrated character, and that it shouldn't be passed off as a meme or whatever. But I guess I don't extensively play Yoshi. He just seems like he has too much stuff, and his weaknesses like lack of flow, grab/grab reward, and roll don't make him not... really good, at least. And even though people were saying this a year ago, I'm still really surprised he doesn't place highly on a more consistent basis. But he does place well every now and then, and his playerbase is without a doubt limited.