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And today, most "Memecoins" are not even coins, most "Memecoins" are tokens. Keep in mind when investing.
The term "meme coins" has been used by many investors and became popular hence, it was called meme coins, but you're right.
Meme coins doesn't have it's own blockchain "EXCEPT" Dogecoin that has it's own blockchain already, and Shiba Inu is the next on the list (based on a quick google search).
I think that the genesis of all cryptos in the meme category being called memecoins could be because the first meme, being dogecoin, is a coin, so the name became a catch for others in the meme category, whether it's a coin or token. I guess what matters to memecoins investors is making quick profits whether it's a coin or token doesn't really matter.
I think that Shiba Inu, is next in line like you said, to become a coin like doge, they're planning to launch their own Blockchain, which is a good innovation by their dev. team. There's a thread about it on this forum.
https://bitcointalk.org/index.php?topic=5495467.msg64042641#msg64042641