I get that the trailing edge plain flap has disadvantages (like tendency to separate flow as I read on a question on here)
Yes, flowler flaps (specifically slotted fowler flaps) are used on virtually all airliners because they provide the best efficiency of all the various flap designs.
The major downside is that they are more complex, and therefore expensive to both install and maintain. But in most large aircraft it's a worthwhile investment.
In small aircraft you may run into the problem of fowler flaps being too efficient. They will have less form drag than a plain flap, resulting in a shallower approach, and also after touchdown you may not have enough weight on the wheels for effective braking, without the help of spoilers and reverse thrust.