The name air fryer is really just a marketing gambit. If they'd tried to sell us "mini-ovens" I doubt they'd have taken off so well.
But essentially this is what they are (with some more expensive options offering other functions such as slow cooking, rice cooking and pressure cooking for example).
As to their value in the home I think it really depends on the type of cooking you do (and if you go for a basic or multi-function option).
If you use your oven a lot (and potentially a pressure/slow cooker re: the multi function options) then you'll get a lot of use from an air fryer. If you mainly use the hob to cook then its value to you is more limited.
Essentially they are less flexible (in their basic form) than a regular oven due to their size - but what you get in return is speed and efficiency.
Arguably the size constraints have also reduced as larger models have come on the market.
If you already have an oven do you need one. No.
But I can understand the appeal for households where the reduced cooking time and cost saving is worth a lot. Equally for people who invest in a multi function option and clear the worktop of multiple other gadgets such as slow/pressure/rice cookers etc or who make the judgement that buying one of these saves buying other kit.
Another benefit is they are a lot easier to clean than an oven.
I don't have one because I have an expensive pressure cooker I use a lot and a small 30cm oven (with a 90cm one as part of my range cooker) that heats up quickly and is perfect for day to day cooking. I don't like slow cookers so a multi function one just wouldn't offer me anything new or better (and I don't want one sitting on my kitchen counter).
That said you'd have to prise my mother's multi function air fryer from her cold dead hands. It's perfect for her and my father in terms of size and gets used daily to cook a wide variety of food. Much easier than bending down to take things out of the oven, to keep clean and cook things quickly.
So I absolutely think they are here to stay as a gadget even if it's not for me (at the moment) and can even foresee as the technology develops people choosing to forgo a traditional oven in their kitchen in its entirety, instead having a couple of air fryers in some built in configuration instead.