Discloser: I am the co-founder (
https://notesnook.com)
We used to ask our users 90% of the standard password requirements (min length 8, 1 special character, 1 digit, 1 capital etc). The result was a lot of people forgetting their password and having a really bad first impression. We were following "best practices" but the user didn't care.
In the end, we took out all the requirements except one: password must be 8 characters long. While we knew this wasn't recommended, especially for a private note taking app, it was a necessary choice because a lot of people either just modified their old passwords or used new ones which they forgot and got locked out. Good security but...if you also get locked out, what's the point? As for people who used password managers, it doesn't matter either way.
A lot of people sign up just to try out the app. Nothing serious. Nothing too critical. If they get locked out after their first usage, it's goodbye from them. I think there are a few things apps can do to improve security without annoying the user too much:
1. Show user a notice inside the app if the password is below a certain strength threshold, recommending them to change it.
2. If the password is reused or compromised, show a permanent warning either on startup or somewhere noticeable inside the app.
3. Promote use of password managers during sign up (and other places)
Ultimately, it should be up to the user to decide if they really want to change their password or risk having their account comprised.
None of these are tested though so I am not sure what the UX would be...