Well, what do we consider to be intuitive..? Coming from DotA, this looks fairly intuitive to me. A blink generally operates in 2 ways: it's instant and therefore this point is moot, or it's associated with a cast time in which case it then depends on how the game engine handles functions to determine whether or not it's intuitive. In DotA a stun will interrupt all actions, meaning casting time is an inherent balance feature for something that's inherently strong (see: Anti-Mage Blink cast time), and in League it's generally used similarly but the game handles the operations differently. A stun (the relevant operator in this problem) does not interrupt cast times in League because then you have some champions getting interrupted during very vital moments of gameplay for their kit, which feels great for the one applying the CC but the person getting interrupted feels cheated by what will essentially be blind chance in 9/10 cases.
League is balanced in such a way that, compared to its predecessor, it appeals to more "casual" players (League players aren't inherently casual, I just don't have a good term for players who prefer less frustrating and punishing gameplay) who don't want the frustration associated with a more difficult and punishing game while maintaining a similar playstyle. For this to be maintained it generally means that the frustration is moved against the aggressor rather than the defender because it tends to be easier to fluster a defender whose defense was busted through by chance than an aggressor who was stopped by the same (this is converse to dodge vs. crit where the general feeling is that dodge feels far worse to go against than crit - for different reasons, but that's a separate conversation unto itself). Most people would rather their defenses and combos flowed smoothly than if they were easily able to be broken by a "Combo Breaker" type of attack.
So then, why is the interaction of Ezreal's blink intuitive given League? Because it's in a game that stepped away from more punishing gameplay and went more towards flowing and forgiving gameplay. Ezreal's E would be unintuitive... if it was in DotA, because if it worked similarly over there then it wouldn't make sense since Anti-Mage has a blink with a cast time and he is stopped. However, Ezreal and Kassadin can both escape Blitz hooks by using their blinks because League is forgiving with cast times, and that stretches for attacks, too. It's worth remembering that a lot of things in this game have a cast time, not just those blinks and Lux's ult. To allow stuns to cancel cast times means that anything with any sort of cast time that gets caught during the stun will be instantly canceled, just like in DotA. But only the vocal people who want less forgiving gameplay actually want to deal with the consequences of changing how cast times interact with CC in this game.
The reason Lee seems like he's so hated by the boards but loved by everyone I know that doesn't frequent the boards? He fully embodies what League is about: fast-paced forgiving gameplay that's easy to pick up and hard to master. He embodies everything they consider League to be.