You'll see that mise recommends installing itself exclusively through package registries: https://mise.jdx.dev/installing-mise.html

pypi, npm, and even github (through releases) are registries.

curl | sh is an anti-pattern. It passes no security check.

There's always the chicken/egg problem of which dependency manager to install first, though. AFAIK there's no "trusted" installed for Homebrew on macOS though I might be wrong.

Exclusively? No, the very first option is the install script, which downloads and unpacks the correct binary for your OS from the Mise website:

curl https://mise.run | sh

...which is the same way Homebrew is installed too.