This is weird.
EES has no effect on leaving the UK by air.
It only effects ferry and train travel because we have an agreement to do Schengen processing on UK soil in those instances.
The delays may happen on arrival at the Schengen airport if a lot of people need to register for EES. Some airports are very organised, have plenty of machines and staff to help, some less so which leads to delays if passengers are struggling. But you are at your destination by then, so no flight to miss, just a delay to getting through to pick up any checked luggage. It took us 15 minutes in Italy in May, but not on a peak travel date.
In theory, once you are registered, every time you enter or leave via a Schengen airport you simply place your passport on the reader and look at the camera to get through the gates, just the same as EU passport holders. This has been our experience. Some airports have separate gates for EU/ Schengen and non-Schengen passports and some of these change the gate category if queues develop. Other airports use the same gates for all passport holders, which, again, has been our experience. Same entering UK at Gatwick.
There may be delays if you are travelling with children as they are generally checked by a human. If there are a lot of families this could slow things down. But again, this is in your destination airport (but leaving as well as arriving, so leave plenty of time when going home).
Border delays at UK airports (in or out) are down to UK border checks, nothing to do with the EU/Schengen..