It's not a burst meta. Burst champions are only good in low elo because players don't know how to play the early game, the mid game, or late game safe. Teaming up is less common giving burst champs easy advantages they shouldn't have. Also, in low elo, players don't like the passive "farm til late game" style of play so they pick champions that are more "flashy" earlier.
On that note, the problem isn't burst champs. The problem is that there is too much damage in the game as it is. Tanks are supposed to soak a ton of damage for their team, but that's it. They shouldn't be able to take objectives or do a good amount of damage to anything, but the overall damage creep coupled with Tanks' kit makes them deal more damage than they should have ever dealt. Now, they buffed the damage on ADCs and mages making the need for MR and Tank items even more necessary.
Mages aren't countered by champions that deal more damage than them. THEY DEAL THE MOST DAMAGE. You can pick any AP champ as support and they can still end up doing more dmg than the ADC if they built full AP. Mages are countered by champions that can get in close to them and take advantage of the fact that they're squishy. At least they should be squishy, but when you have items out like Zhonya's that just says F all damage or kill attempts, Banshee's Veil that says F your CC and AP, and various other AP items that grant 200+ health like they're some tanks, then their counter becomes less and less of a counter. ADCs get supports that keep them alive and their items and Keystones deal an extreme amount of DPS while giving them the utmost mobility making a competent ADC uncatchable unless you have a champ that can straight dive them in an instant.
Take Poppy for example; If you get a competent Poppy player who farms it out and builds nothing but tank, she can virtually one v one anybody and win without taking a lot of damage. Sejuani is another example. There's also Sion. Not to mention Ornn. The list goes on. I say this not to show how great tanks are but to point out the fact that they are dealing too much damage. But for the amount of damage they have to soak at all stages of the game, they are very squishy. They recently buffed ADCs. Mages have items that can melt tanks in one combo.