When she was alive, my 90 year old grandmother would use the wheelchair service because it would simply not be possible for her to walk the 200 metres with her cane. That being said, whenever we flew with her, we would always let the agent take her in while the rest of our family boarded normally with the rest of the economy passengers.
Note: My grandmother did not speak a word of English. She lived through WW2 eating bark off a tree, I'm sure she can sit and wait. She never liked being pampered.