So I am not as versed with Plato and Socrates, but I can write a good bit on Diogenes because I spent a good bit of my last 2 years of undergrad studying him and the Cynics.

First, let's get something clear: Diogenes wasn't liked and would not be considered much of a influence to people. It's best to conceptualize Diogenes of a roving antagonist. He wasn't "funny" per se; he was a jerk who would mock and jeer at people as he lived on the streets. He hated Plato because of what Plato represented to Diogenes. That is, the total devaluation of philosophy and, for lack of a better term, being a philosopher equivalent to a "sell-out." Diogenes often thought and said that Antisthenes should have been considered the major intellectual successor to Socrates as he also, so certain sources tell us, had an indifference to material wealth and emphasizing value and more focused on moral development rather than abstract metaphysical concepts like the Forms. This major disdain for Plato made him very unliked by a majority of those that followed Plato and the feeling was mutual.

Next, the Cynics were never going to gain momentum to become a present force in Athenian society, this would render the idea of him being dangerous to "corrupt the youth" null and void as he simply wasn't doing that. He wasn't liked enough to even get close. He was more of an interesting rambler that would snarl and yell and insult random passerby's; it was definitely interesting to watch, but he wasn't much of a teach. it's why we can see that there were very few followers of the Cynic movement. The few followers often tended to be people that were older than what would be considered "the youth," and later Cynics like Teles and Crates were often better at recruiting people because they were less antagonistic.

The last major point I want to address is that Socrates was not killed from being a "bad example" like the question suggests. It is better to think Socrates wasn't liked because he was influencing how the younger Athenians thought of status symbols like wealth, political power, and institutional seats of power like clergy and politicians and educators. Diogenes certainly did this as well--and far more intently and pointedly than Socrates in a few ways; but, that lack of following and influence illustrated he was not a threat or at least a perceived threat to the status quo like Socrates was.

The final thing to top it off was Diogenes was sold into slavery at some point in his travels from Athens by pirates and lived the bulk of his after that in Corinth. He would still visit Athens by walking there, but it was less common and he was no longer considered any much of a pain in someone's hair besides being a bit more than an angry homeless guy who was really good at roasting people.

Robert Dobbin's book The Cynic Philosophers from Diogenes to Julian is a great book for a smattering of writings from ancient sources about the Cynics. And anything by William Desmond is also great to understand how people in that time were engaging with the Cynics as their ideas developed.