It's a common known fact that passengers travelling on domestic flights, especially business people, will not arrive for their flight more than 2 hours before their scheduled departure time.
On the other hand, passengers travelling further afield will.
Lo-cost, I.E BMI Baby, pay for their desks to be open 2 hours before departure, it saves them money.
Charter pay for 3 hours before departure, it makes the check-in experience better for the passenger, or the aircraft is larger.
Long Haul pay for 4 hours before departure, normally due to larger aircraft size.
In reality, if your holiday flight abroad departs at 5-7am, your not going to want to sleep the night before, before making the trip to the airport for a 3/4/5 am check-in. Especially if you have some distance to travel. This is one reason why you see passengers early at the airport. However, this is a small minority, of which can normally be checked in within minutes of the check-in desk opening at -3.
Baby often have a large queue in the early hours, if baby payed for their desks to be open at -3 instead -2 before departure, the queue wouldnt be as bad by the time the desks open. The deciding factor on queue's boils down to departure time and destination.
You dont see huge queue's for the FlyBe domestic flights at -2.
Handling agents need to effectively manage their staff. If they are going to provide an extra agent for longer than the contracted times, i highly doubt the airline will stump up the cost.
Why pay for another agent to be open, just to check in a couple of passengers who have arrived early. This in turn means you need to provide extra baggage handlers to process the bags, extra security agents to process the passengers once checked in, will the shops want to open earlier?
In an ideal world, its great customer service, and for the airport its great as it provides better passenger flow, the less time passengers are queueing, the more time they are speding money in shops. However, in a cost minded tough industry, its not cost effective.