The main advantages I see that it's yours: no account, no free tier limits. Also since it's open source, if it doesn't do what you need, you or anyone else can add it and everyone gets it. As most creators on itch can program quite well, I think it can work.
That said, if you want a top 10 running in five minutes and don't care where the data lives, a hosted service is less hassle. It's a trade.
What have you been using for hosting leaderboards?