In the past that's exactly what they've tried to do, and this usually ends up clobbering the law-abiding users in the process. Most of these bands are pretty close to each other - the 10M HF band is right next to the CB band, the 2M band is right next to the emergency services bands and pretty close to both the aviation bands and the weather radio bands, and so on. Gear from one will pretty much just work on the nearby bands, absent some other protection. You can do filtering, but it's physically pretty hard to make an amplifier work ideally within its band and then immediately stop working when you take it outside its band.
So the FCC's response in the past was to make it illegal to produce anything that could go from [unlicensed power level] up to [licensed power level] on demand. If you wanted to make a 10M amp that could hit say 150W, you had to require at least 75W drive power because that was beyond what a legal CB radio could deliver. Kinda sucked for anyone who couldn't afford a radio with 100W of drive, and I think they eventually let off a bit because they were losing the battle to cheap Chinese junk sold over the internet. They're very proactive about enforcement, they'll get you sooner or later, but until then it's better for everyone if you're not spewing harmonics everywhere.
There are radios and amps that use a frequency analyzer to automatically cut out when operated out of their intended bands, they're just very expensive compared to most of the gear that's out there. And a lot of the Software Defined Radios and so on are actually wideband radios that are physically capable of operating across a bunch of bands. These are very concerning for the FCC, and you pretty much cannot limit these physically, it has to be built into the firmware or the controlling software. Hence the article.
There's also just different rules for different license classes. As a radio amateur, I can also use 2.4 GHz (13cm band) under my license, and I am allowed to operate with up to 1500 to 2500 watts EIRP depending on mode. That is of course subject to lots of limitations including "minimum necessary power", but there's nothing physically stopping you from taking a 13cm amp sold for radio amateurs and running wifi over it. Same frequency, how does the radio know?