Not the case on many Android browsers, you can present the user with a button to do this for them by listening for the `beforeinstallprompt` event. There are some requirements to meet for that, but it's a pretty user-friendly way to push your PWA to the home screen: https://developer.mozilla.org/en-US/docs/Web/Progressive_web...
I’ve worked on projects where we ran this experiment, and the success rate of “install this app and click on it” is several times higher than “navigate to this webpage every time you want to use our tool”.
One small correction though, android has made it easier to add a “progressive web app” to the home screen now. You can prompt the user with a dialog asking if they want to install it. I think there was at least some period where Google was really encouraging PWAs. iOS still sucks. I’ve had very poor success rates in getting users to install our PWA using the iOS workflow (and our tool is something they need for their jobs, so they are highly motivated to install it).