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I have noted that all the airports I have visited have had "attendant-propelled" manual wheelchairs that may only be moved by an attendant:

source: Wikimedia Commons.

Rather than the more traditional manual wheelchair, that can be propelled by the user or an attendant:

source Wikimedia Commons.

I've not had personal experience with needing a wheelchair (in an airport or otherwise) but it seems to me this would be incredibly frustrating.
To be completely dependent on another (be they an airport employee, or a friend/family member) to move, seems utterly awful.

While not needing to self propel between gates makes sense (and is obviously often required) not being able to direct your own movement without asking someone else (for those who normally can), during a six hour gap between connecting flights seems really problematic. Not being able to go into the bar or slowly browse the duty free on your own to kill time.

So why not have the manual chairs that can be attendant or self propelled?
Is it a matter of cost?

Which seems off given that airports are such a high expense area/luxury anyway.

It is a matter of design?

Perhaps difficulties in make a user propelled chair narrow enough to get through aisles?

Or maybe difficulties in making the transfer to/from the wheelchair to the plane's seating when using a normal "big wheel" chair?

Lots of airports have traditional style wheelchairs. The first one you show is specific for boarding an aircraft.

But they restrict use primarily to airport personel. One it controls where chairs are staged , two it limits liability.

I had to avail myself to chair service once and was glad to be pushed. Not being used wheeling myself around, traversing a big airport like Atlanta,Tokyo, etc would have brutal. And the attendant was fine taking me to a lounge, then returning later to wheel me to the gate.

The simplest way to answer this is to look at who would need that wheelchair and why.

Typically planes don't have space for a wheelchair down the aisles, so disabled passengers have to use a special wheelchair on the plane, pushed by attendants. There isn't an alternative to this (unless you use a stretcher instead, but then you have a whole new set of problems).

In the airport building itself, many airports allow the use of your own wheelchair up to the point of board, when you have to change over and your own wheelchair is put in the hold. In that case someone with a permanent disability won't need an airport wheelchair in the terminal. Only people with a temporary disability/injury or people who are physically frail would need an airport wheelchair then - and both of them will need someone pushing them, because a manual wheelchair is something that you need to build up sport-specific muscles for.

If the airport needs your chair put in hold luggage immediately, then of course you're stuck with the airport chair all the way through the terminal. As before though, this is only an issue for permanently-disabled people who are regular users of a manual chair - everyone else would always need an attendant anyway. Typically this is the situation for smaller airports or airports in countries which are less well-equipped for disabled passengers. In that case, putting the responsibility for getting you around directly onto an airport employee (who has to stay with you for the duration) makes life very much easier for the passenger.

Since my GF broke her hip last year, I can personally testify that the loss of independence is a very big deal for people in wheelchairs! But it's essential to be practical to adjust to the new situation, and part of that is the wheelchair user accepting that some things may in fact be impossible without assistance. I'm not saying this is something anyone should enjoy, or that it isn't frustrating! Just that it is the physical reality that needs to be lived with. (Of course it's also a physical reality which able-bodied people should be aware of, so if someone's coming through in a wheelchair then give them room - they've got enough crap to deal with already, without you getting in the way.)

Really a comment but it won't fit:

I have had a bit of experience with airports and wheelchairs after my wife was injured on a trip.

The chair in the first picture is intended only for boarding and on-board use. Note how narrow it is--there are definite stability issues with it, especially if faced with any bumps. The transfer between a normal wheelchair and the airplane chair is made at the end of the jetway, the last space where there is reasonable room to work. Stability is not an issue once you are on board, there's no way it's going to tip over when you are between the seats.

The regular chair is used to get around the airport. I do not know how it works everywhere but in Los Angeles apparently those regular chairs were assigned to the attendants--and it took raising a stink to get him to find another chair for her rather than leave her effectively immobile at the gate for the 5+ hours of our connection. (I don't think anything would have been done had she simply refused to get out of the chair until a replacement was found.) While for the most part she did not want to move (the problem was a soft-tissue injury, any movement of her lower back was quite painful) that's a little long to leave someone without access to the restroom!

There are two types of wheelchairs provided at most airports. The traditional self-propelled ones you mention are often used by those passengers that need assistance walking long distances but are able to walk for short periods of time.

For example, my mom uses these all the time at large airports because of her knee surgery she cannot walk at a normal pace so she requests wheelchair assistance, and they always bring this normal one for her.

The second type (attendant only) is used for those people that have very little mobility and it is specifically designed to be used on board aircraft - as its reduced width allows it to be wheeled down the aisle.

My mom doesn't need these as once she arrives at the airplane door, she can walk down the aisle to her seat.

In either case - the wheelchairs are accompanied by an attendant from the airport services (very rarely is the attendant from the airline). Even if someone else is pushing the wheelchair, the attendant always accompanies the passenger to expedite them through security / immigration and place them at the appropriate area of the gate for priority boarding.

I once made an airplane trip where I used a standard wheelchair in the airport at either end. It was my only time using a wheelchair; navigating the airport on foot would have been very difficult, and operating the wheelchair myself would likely have been almost as hard. (I was able to walk through the security gates with a wooden cane lent to me by the TSA, and to slowly walk down the aisle of the plane once I had been wheeled to the door, so I can't speak to the aisle chair pictured.)

I assumed that the wheelchair was supplied with an attendant due to liability issues. (I had someone travelling with me who was able to push the chair when we did not have the attendant. Not everyone is so fortunate.) (The attendant claimed that he was not paid and working only for tips; I don't know whether that was true.)

An airport would be a terrible place to learn to operate a powered wheelchair!