The main downside [for a 9V battery] is that linear regulation is inherently wasteful and you lose (4V x your current) to heat. They also have a comparably low capacity compared to AA's so they're not the best choice for a long life application. In that case you're better off using a 95%+ efficient switch mode supply, but then if your system requires low noise you have other considerations.
It's not cut and dry!
Funnily enough, I've never seen a stacked 9v as pictured in the article. The few that I've opened up have had elongated cells laid out like a six pack of beer.
Bear in mind that 9V batteries also have far easier interfaces than AAA packs, requiring a single plastic/metal tab rather than an injection moulded retainer. In some cases, the price difference for both manufacture and battery cost makes it worthwhile.
As for current, plenty of devices run under 20mA happily. A microcontroller in active mode will probably use under 15. Most 9V devices aren't used continuously, my IR temp gun uses a single 9V for instance. However I've also seen smoke alarms and other home sensors that use them.
I'm not disagreeing with any of the criticism here, I would never use a 9V batt in a project, but there is good reason to consider it and people should understand why so many products still use them.
Stacked 9V batteries are typically the old Alkaline sort or rechargable.
Not many people know this, but it's now possible to get lithium, secondary (aka "rechargeable") batteries. They really put out about 8.0V, but sub swell in many apps.
And have ~70mA constant discharge rate.
I've been enjoying using them in many applications, esp with a buck-switching regulator.
Or no regulator at all if you use 4x AA NiCAD or NIMH.