Here's a quick but efficient bandaid for the [Burst<DPS>Tank>Burst] problem:
Add a bonus armor penetration on critical strikes and decrease the critical damage AD scale.
I know that other people already suggested this, but it definitely would be a very good way to align the [Burst>DPS>Tank>Burst] cycle; such core/big problem will not be solved with slightly-hard changes like the new runes and base stat changes, since they will not affect heavily the main aspects of the issue (Crit dmg and items, assassins's delay and viability, life steal mechanic). This way, the cycle would be fixed for a while, giving time to the dev team elaborate a better solution.
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A quick example with [HYPOTHETICAL NUMBERS] -> Without Infinity Edge: Critical Strikes deals
200%->150% of total AD and ignores 40% of target's bonus armor. -
With Infinity Edge: Critical Strikes deals
200%->175% of total AD and ignores 60% of target's bonus armor.