It's not easyJet staff at the gate, it's the handling agents staff.
The payment of £16 goes to easyJet for your infant to fly, not to the handling agents. That £16 covers the cost of fuel that the little one might be causing the aircraft to burn during the flight (remember all weight onboard increases fuel burn).
Handling agents only provide a limited amount of staff at the gate, who have the job of checking the boarding cards which is a job that is very intensive as easyJet (and any airline for that matter) do not want to take the wrong pax to the wrong destination. The gate staff are also reconciling the boarding cards to get the correct head count. If a gate agent was to move from the gate and assist with carrying items for pax down to the aircraft then they would not be doing their job of checking boarding cards and reconciling boarding cards and trying to supervise the boarding process.
Your wife did not need to carry the pushchair down to the aircraft, it could have been left at the gate and the gate agents would then ensure that it goes into the hold. This happens at all airports where those parents travelling alone with an infant do not then have to struggle down to the aircraft with half a tonne of stuff.
Remember, the only easyJet staff you will ever meet are the cabin crew that are onboard the aircraft. The cabin crew want you to have a pleasant flying experience unfortunately though, it's always the handling agents that create the negative experience for the pax.