You bring up a good point with other lint hook compatibility - I had overlooked that my lint features require a specific print function to work. I've made an update which will replace print with the custom lint version so that other lint hooks can also print to the final file. I'll update the itch with it sometime this weekend.
As for closing the game - this is more out of caution than anything, as I do modify the internal AST nodes when running lint (the built-in linter does also; it runs a separate version of your game to lint). You're welcome to remove the line renpy.exports.quit(save=False) towards the end of the custom_lint file, but I make no guarantees on behaviour. I suggest instead that you just launch another window of your game to quickly run the lint, as it won't close or affect any previously-open windows of the game aside from the one which ran the lint operation.
Otherwise, the main feature offered in this linter which you won't get with the built-in linter is properly linted conditions. Turning off warnings for text tags will hide that particular warning about unknown or unclosed text tags, but the built-in linter doesn't know what inline conditions are and therefore can't properly evaluate that something like {if apples => 3} is malformed (it should be {if apples >= 3}). You would need to run through the game and get to that particular line (which would likely cause a crash) to find out that it's incorrect. There are different levels of strictness you can enforce through the custom linter which will do things like flag if you haven't properly defaulted a variable before you use it in an inline condition.