Pepe is like the standard form of response images that preceed time and relevance itself. Though it may not seem as such on the general web, in 4chan, that frog still thrives like maggots in a roadkill. It's versatility and wide variety of usage is what helps to its age.
Paradoxically, Pepe is virtually ageless. He's not a meme, but a template of a meme. He can be representative of anything that sits on the absolute edge of any topic. You got Nazi Pepe, you got suicidal Pepe, you got white supremacist Pepe, you got trump Pepe, you got Islamic Pepe, you got Christian Pepe, you got the OG vibin' Pepe, you got baby Pepe, you got fat Pepe, you got Pepe shitting on crying Wojak.
Fuck, we even got she-Pepe.
And even then, despite being a blank slate, Pepe still stands as a meme with character and personality, due to the usage of Pepe in the past (mainly by QuattroChan) that brought so much history to the meme that it's earned its own character that unconsciously goes with every new type of Pepe that comes along.
Pepe the frog is popular because of how both ironic and satire its usage on 4chan had made him to be, allowing him to break taboo and represent even the most degenerate of stereotypes. You might already be put off by the KKK Pepe I just mentioned but oh boy, that's just the fucken tip of the ice berg.
You can see Pepe for what he is on face value. You can go ahead and make a gay pride Pepe, though that may set the /Pol/ board of 4chan on fire (in second thoughts, do it. shit's getting boring over there I wanna see something worthwhile happening). He's so versatile and easy to use that anything can be Pepe.
But mainly it's funny due to its low comedic value but high relevancy in culture. He's not meant to bring comedy, but be a caricature towards topics. Hence, a meme in its simplest form.