I don't necessarily have a problem with dashes as a whole, (though I do love the big, immobile meat-wall type of character the majority of times in any game I play) but I DO have a problem with dashes/hyper mobility with little to no trade-off.
Shaco is a good example of mobility with a trade-off, or is meant to be, anyway, when the current damage climate isn't allowing him to 1 shot you from full hp. He is an opportunistic assassin who requires setup. When I picture Shaco killing someone, i envision that ADC who survived a close scrap with 30% hp getting gibbed while backing in a bush because they didn't respect the clown. The other scenario I see is the enemy jungle chasing the low hp Shaco into his own jungle, but doesn't realize he's being baited into swarms of boxes, and ultimately gets tricked and whittled down until he can be finished off safely.
Now picture LeBlanc. How does she kill someone? Q>R>W dead. All in an instant. No setup, just be in range and have your cooldowns. What is her trade-off? Low hp? That's countered by an auto stealth baked into her kit, and has no skill requirement.
Pure mobility itself isn't the issue. Mobility with no trade-offs, or simply the semblance of trade-offs, is. It makes playing a mobility character, or someone who enhances that character (Malph/Ali with Yas) a requirement to win.