Running a controlled experiment is hard. In some domain it is harder or even impossible. Here are example
If you want to introduce a new button for volume up/down on car steering wheel. It is very hard as changing hardware on car takes years. Same is true for TV/mobile phone.
If you want to try new technique in medical domain, you may not be allowed. (as it impact people life)
If you want to do safety test on car, you cant run online experiment. You need to use simulation.
There are many reasons where online experiment should not/can't be done. However there are alternative approaches that can be sued. Learnings and concept from ab experiment still apply.