"universally applicable" is correct and usable in written English. You can use it to describe something that is true, useful, or relevant in all situations and applies to everyone. For example, "The Golden Rule is a maxim that is universally applicable.".
The UN wants the SDGs to be universally applicable.
The Bush administration did not originate the conviction that American freedom is universally applicable.
I am not at all sure these designs are going to be universally applicable.
We may also need to accept that treatments for mental disorder are not universally applicable.
These are so oblique that they are universally applicable: anyone could find meaning in them.
The lead narrator Andy's moaning also began to seem less superficial and more universally applicable.
It was a universally applicable technique that deepened the interpretation of any song in any setting.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia