My burger cooking is usually done on a propane grill (I'll fire up the pellet grill for steak and such, but not burgers unless I'm cooking for company). Preheat time: about 8 minutes. Then 5 minutes on side #1 followed by 4 minutes on side #2. So about 17 minutes total, including grill preheating. And I can easily see them to tell when they are done (or course, I supposed you could pull the basket out of an air fryer too, when you wanted to check. If you want faster burgers, buy one of those George Foreman grills that cooks both sides at once. They actually don't come out too bad out of the Foreman - I do prefer flame grilled, but Foreman is a reasonable substitute when it's snowing outside.
As far as healthy, what comes out is only going to be as healthy as what goes in. If you're going to cook frozen chicken nuggets, an air fryer is not going to turn those things into something healthy. Compared to deep frying them, sure, they will be "more healthy than deep fried". Duh. But they won't be any more healthy out of an air fryer than they would be out of an oven. I think when they are advertising "healthier foods", they are only comparing it to the deep fried equivalents. As one who never deep fries, an air fryer would be no more healthy for me than my normal cooking methods. I would have to buy one for some other reason than health. The foods you see mentioned for air fryers are a lot of times: french fries and chicken wings. And a lot of snack foods (fried cheese sticks, etc.) I'm sure air fryers will cook a whole lot more. But I'll bet a lot of people don't advance much past wings, fries and snacks. Since I eat these seldom, an air fryer might entice me to eat them more frequently. (Clarification: I do eat a lot of snacks, just not cooked snacks). Additional eating of non-healthy stuff just to make use of a new kitchen toy is not healthier. It is just the opposite.
Health is not a reason to buy an air fryer. Unless you normally deep fry everything, and would stop doing that if you had an air fryer.
Since you all have intrigued me about these air fryers, I've been looking myself. What I've come up with so far is a positive and a couple of negatives. The positive: The crunchier foods that come out of them sounds mighty appealing! The negatives: You can only make small batches of food in them, even the larger ones. Cleanup will be a pain compared to what I'm used to, possibly a major pain. Counter space used, you need a lot of it otherwise you'll have to store the thing in a cabinet and probably forget about it. Noise, from what I've read some of them are really bad. Most seem to be "about like a vacuum cleaner" per reviews. I don't know about y'all, but we turn off our vacuum cleaner if we want to have a conversation. They're not deafening like some chainsaws, but they're not comfortable conversation partners either. Air fryers cook you food faster than a regular oven. That is a positive. And the flip side of that is that I'd need to re-learn how long to cook my foods for, which has been somewhat ingrained in my brain for decades. That's a negative. Cost is not a positive or a negative. If you don't have disposable income, you shouldn't be considering buying a kitchen toy like this in the first place. Nobody needs an air fryer. They just want one.
All the negative sounding comments above aside, I am still actively looking at buying an air fryer. Because "The crunchier foods that come out of them sounds mighty appealing!"