I think the idea of implementing delays to burst on assassins was a good one, even if the specifics of the implementation weren't always great (LeBlanc in particular has suffered a great deal for her clunky new innate). What isn't so great is that damage in League has an absolutely huge amount of variance, to the point where the same champion, when ahead, can deal a literal multiple of the damage they'd deal if they were behind. This means that many DPS champions easily become bursty when they get a lead, but it also explains why AD champions are more likely to have less counterplay to their burst than AP champions, irrespective of items like Duskblade: building AP means your damage is almost completely defined by your kit and its limitations, whereas AD can always at the very least be expressed through autoattacks. Therefore, while an AP burst champion may be able to output too much damage if they get too far ahead, if their burst is meant to be delayed, it will always be delayed no matter what. An AD champion, however, can just autoattack whenever, so even if their kits also have delays built into their damage output (like Zed's ult, for example), those delays can be bypassed.
In an ideal, balanced world, the lessened impact of ability gating on AD champions would be more or less fine (it should be okay to have a playstyle that involves weaving continuous attacks in-between bursts of damage), but the current problem is that damage is incredibly unstable, as it often heavily relies on item purchases, and therefore induces a very large degree of snowballing: if a champion gets ahead, or in certain cases just reaches their late-game build (or something close to it), the innate counterplay to their DPS-based damage vanishes as they begin outputting burst per second. If they happen to fall behind, they often cannot function properly at all, because the only way they can get a lead is if they get kills, which require a minimum damage output, which requires items, which require gold, which is heavily conditional upon having a lead in the game. We are in a game state where some champions effectively become incapable of applying some of their core contributions in any meaningful amount, simply because they fell behind. This is made worse when there are heavy amounts of low-cost shielding or healing (e.g. life steal), which further negate what little damage gets outputted.
This issue of vast differences in fighting power is why I'm not a big fan of stats on items. Passives and actives have merit, as they add gameplay, but stats do not, and at this point only serve to make the game more snowbally. There was once a time when stats were promised to offer complete variety in playstyle, so that champions could realistically go for AD, AP or health builds and succeed, but at this point champions are essentially forced to go for the same core stats in every game, and are balanced around those, to the point where the only variation comes from item-specific bonuses, rather than their raw stats. I think it would help League significantly if there were much stronger upper and lower bounds on a champion's statistical power: even if not everyone may agree to removing stats completely from itemization, I think most of us at this point can agree that it might be better to shift at least some focus away from pure statistical power in fights, by lessening the stat differences between players that are behind or ahead.