From what I've read, the main reason not to use tempered glass is because of the way it fails. With regular (annealed) glass (or heat-strengthened glass), when it's under pressure and part of the glass is subject to minor damage - such as a small crack - you usually have time to drain the tank and replace or repair it, as the rest of the glass holds it in place pretty securely (essentially, the crack has to spread some ways before the glass pane breaks and total failure occurs). With tempered glass, when it's under pressure and is subjected to minor damage, that damage results in catastrophic failure, and the damaged pane bursts. As I understand it, this is why it's alright to use for nano tanks, but not for larger tanks.
The second reason not to use tempered glass is that it's usually more distorted than annealed glass as a result of the tempering process (meaning the viewing quality would be lower for our tanks).
That said, to clarify one point in that article (I skimmed it, I didn't read it in depth) - tempered glass is significantly stronger than annealed glass of the same thickness (~4-5 times stronger).
These things are largely why aquarium companies use tempered glass for the bottom panes of our tanks - we don't typically see the bottom, so there's no need to worry about the optical quality; there's a relatively low risk of damage (the only times I've heard of bottom panes being damaged are when loose rocks fall in the tank) and it's held relatively securely in place when it's the bottom pane (meaning that even if it breaks, the glass is still more or less held in place, so I'd guess - though I don't know for certain - that it would leak horrifically, but it likely wouldn't be an instantaneous dumping of the entire tank's contents to the floor); also, it's much stronger and lighter, so they save on shipping costs while still producing tanks capable of holding the same amount of water.
This link from a UK glass company specifically tempered glass, heat strengthened glass, and heat-soaked glass, but the information in it gives one an idea of why tempered glass generally isn't used for the side panels of our tanks:
