I'd be doing everything to ensure that baby boarded the plane in the least stressful way! Nothing worse than a stressed-out baby in an enclosed space.
In my opinion, you are naive or lucky! We don't fly with DD very often, but sometimes we think, well she is entitled to nice holidays too; or there is a family wedding abroad. We would pay for priority check in. I would not be at all happy to see a set of parents with a 3m old baby go to the head of the queue, as they think they are "entitled"; when DD may not be able to stand too long - we could end up in A & E and miss our flight. As for the pp, who say we are not taking into account how much stuff parents need for a baby - I'd say some of us, need the same stuff for our DC; but its adult sized. Incontinence pants, baby wipes, nappy sacks, meds, spare clothes, food, something to keep her occupied on the flight.....
I can assure you, it is far harder to deal with an adult sized toddler, with challenging behaviour, than a 3 month old baby. She can be charm personified; but she can get stressed too. No baby is capable of shouting at all and sundry
"I hate you. Fuck off you bitch. I never want to see you again!"
Then, perhaps, she could push you over or punch you in the stomach for good measure.
I will certainly book special assistance for her in future (although we have booked it before, and on the day, there was none); now I know people with babies think they are the only people in the world, with difficulties in queuing; and apparently unable to conceptualise that other people have problems too.