Non-allocated seating gives passengers an incentive to ensure that they arrive at the gate ontime or early, and it is my experience having handled airlines like easyJet & Ryanair that this is generally the truth, with fewer passengers having to be looked for at the last moment. The problem is that with this system it can be incredibly hard work for the gate agent, ensuring not only that the pax that is presenting themselves to you has the correct ID but is also in the correct boarding group, because sometimes as soon as you put out a call, a surge of people come towards you, or whilst you're setting up the gate, there are people hanging around you, which is rather irritating. I think it helps if you say "Ladies & Gentleman, can I have your attention please, and please remain seated. We will shortly be inviting passengers in possession of boarding cards ..." Irather than "Ladies & Gentlemen flight XXXX is now available for boarding for passengers in possession of boarding cards ..." because as soon as people hear a flight number the rest of the announcement is drowned out or doesn't mean anything.
I agree that whilst ensuring everyone is at the gate ontime, and proceed through the gate quickly, it is not always the fastest system. Open seating encourages people to mill around in the aisles finding the perfect seat, with some actually sitting in aisle seats to try to keep the centre one free. Passengers spend longer times in the aisle deciding where to plonk themselves down, rather than knowing exactly where to go. If boarding via stairs, it also leads to people congregating around the front set of stairs, causing a blockage.
Having handled go before it became easyJet, I can honestly say it was just as easy to ensure a 25/30 minute turnaround with assigned seats as it was without. Assigned seats make the experience far more enjoyable for pax who are travelling with families or who have a particular seat they desire. Assigning seats is for some low-cost airlines an additional revenue stream as they charge a small amount for a pre-assigned seat, and no doubt there would be people willing to pay for this service. Nevertheless, I wouldn't say from a staffing point of view one is easier than the other.