I'd be curious to know which tech stack you're using where you even need to use wait for it.
I've built and worked with various Flask, Django, Rails and Phoenix apps and none of them needed wait-for-it. Most of those ran a web server + background worker + redis + postgres.
Everything starts up no problem in development without any extra tooling when using Docker Compose.
Tests in CI are a different story, but I find wait-for-it to not be the tool to fix that problem. Instead I ended up writing this tiny shell script[0] to wait for a process to be ready between running a docker-compose up -d and running my test suite in CI. You'd run into this issue with or without Docker Compose too.
You could use it to wait until you can do a SELECT 1 on your database (the docs cover multiple database examples). The docs also cover why wait-for-it doesn't work to fix waiting for a database and other common use cases.