The reason AD assassins/ADCs are stronger than AP assassins/Mages

Auto-Attacks.

Think about it, an AP carry does their combo within 2-3 seconds at most and is basically silenced from doing a full combo again for about 3-4 seconds. This gives time and counter-play options to the enemy team on when to dive them or when to engage. In addition, if that AP carry decides to build magic penetration or Liandry's then the effects do not last very long after their combo.

In contrast, AD assassins/ADCs do not act this way. They can deal a full combo and still deal just as much damage as a tank or fighter after it is done. Once their combo is finished they can still chunk down other front-line champions with the armor penetration/critical strike/botrk/attack speed items that most usually build. Therefore, they are filling two roles rather than one. They can burst a squishy safely remove themselves to safety and then dive right back into the fighter either peeling with AAs or simply dealing a significant amount of damage from % damage health/armor penetration items alone. Mages cannot compete, their damage comes more from their abilities and combinations rather than AAs so this puts them on a limitation of damage or counter-play solution (cool-downs).

There needs to be a period of time that fighters and tanks can use their advantage in a team fight to crush assassins.

It is not the champions themselves, not usually; it is most likely the item combinations that allow these champions to do ridiculous amounts of damage in both burst situations with their kit and with mega sustained damage with their auto attacks.

In Season 3, the solution to armor/magic penetration stacking was to build health, this way you could survive their full burst combo and then win a sustained duel; however, this changed during Season 4. Now assassins and ADCs deal just as much burst damage, but then win the sustained duels because of BOTRK. There is no counter-play item for this combination. Tanks/Fighters can no longer build MR/Armor to counter BOTRK, nor can they build health to counter the armor/magic penetration items. Both become useless.

Just my two cents from thinking in the shower this morning. What do you guys think?