How to indent every paragraph, excluding headings?

This doesn’t answer your question of will you regret using the native styling, but if you want “fully” indented paragraphs see if something like this works for you:

#show par: it => [
  #set align(right)
  #let indent-amt = 1em
  #block(width: 100% - indent-amt)[
    #set align(left)
    #it
  ]
]

Some styling rules might not work as they did before because you are now inside a block instead of a par, but it does e.g. indent after tables