Thanks for the long post. I hope you had a good Easter/Passover too. = )
About mages needing burst to be rewarded, I think it's fine for specifically Burst Mages and AP Assassins to specialize in burst. I don't like when other mage classes feel too similarly burst-focused due to a lack of alternative item paths and the prevalence of flat magic penetration in almost all AP builds. I would like for champions like 
, who are not considered part of the burst mage class, to have different items available to build that would emphasize different strengths. For example, could build new items that specifically increase the size of their area of effect abilities, provide a ramping buff depending on how many enemy champions are hit within the last few seconds, or apply non-stacking damage over time effects that would also reward hitting a large number of targets to keep the DOT active. could benefit from the non-stacking DOT effects too, which would reward his sniping/poking playstyle and he could also benefit from the ramp-up and AOE items to improve his ultimate and teamfighting abilities. could really benefit from ramping up DPS items to reward them for kiting and landing multiple abilities (or keeping Voidlings on a target), so they could use some sort of item that grants a ramping-up buff for hitting the same target repeatedly, allowing them to specialize into marksman levels of DPS to slay tanks/juggernauts.
But all of these strengths would need to come at a cost so that balance is maintained, so they would need to give up burst/flat-magic-pen when choosing these new items. For that reason, flat magic pen would need to become harder to add into a build. I'll come back to this.
Taking things to an extreme level of specialization, we could even get an item that actually directly reduces the owner's upfront burst by converting some of their instant damage into a larger amount of delayed DOT or stored 'damage charges'. We do currently have a few items that provide some variety, like 
, but we could do with a lot more. 
and/or 
might be a good fit to turn into a delayed/ramping DPS item. Some sort of 'Curse of Kumungu' plague artifact would make a good fit for a debuffing AP item that inflicts the enemies with disease, making them take increased magic damage from the owner and causing the enemy to have reduced AP/AD while receiving DOT. Some sort of 'Terra Breaker' infernal gauntlet item could grant increased AOE size, where AOE abilities cause fissures to tear open along the radius and deal a % of the spell damage. So if you wanted to be a specialized AOE mage, you'd likely want to get Terra Breaker and then apply Curse of Kumungu and Liandry with your larger AOE. You'd likely also want Rylai and possibly one of the reworked DPS items .
By specializing like that, you should no longer have the AP or flat pen to burst down enemies, but you would likely perform better in teamfights and better against tanky enemies as a fair tradeoff, especially with a 
if the enemies are stacking MR. To ensure that tradeoff actually exists, flat magic pen would need to become harder to justify in a mage build. I think that 
should be changed to grant some mana and +5 MS per 100 AP (max +20). Lethality should then become a neutral/hybrid stat that works with both physical and magic damage and a new pair of 'Bilgewater Boots' could be added with a relatively weaker amount of lethality (maybe +9 or so) as an option for either AP assassins or AD assassins and certain burst mages. 
could become an AD/AP neutral lethality item, with higher lethality and no AD. 
could lose its magic pen in exchange for more AP and/or a lower cost so that it is clearly a counter-sustain item and not a burst item. Some new AP lethality items could be added, possibly building out of 
which could become the AP equivalent of 
. For example, 
could gain lethality as a stat and have its build changed to 
+ . Certain AP champions, like 
could be granted compensatory lethality ratios like 
has to help them adjust to their new builds and to also create a new balance lever to prevent tank from resurfacing in the future.
It would be possible to go for an AOE burst build too with Terra Breaker, 
, and lethality items. That would be an attractive option for 
. The main point of the changes would be to increase playstyle variety by creating new options so that burst and flat pen aren't nearly universal for all types of AP champions.
could have their AOE all increased and their single-target DPS lowered to make them less homogeneous with other marksmen)
mid/jungle 
to maintain their total class pick rate is fair)
to leave top lane (I don't want melees like 
to go bot lane either so it isn't melee favoritism; many ranged vs melee lane matchups are very toxic, with the exception of assassin mid-laners when they are balanced around needing to roam)
synergizes specifically with marksmen