To answer why high elo players don't always grab every time they can, sometimes it's situational. If you can grab someone from under their turret, but your adc is closer to the middle of the lane farming, you aren't guaranteed a kill. Then there's the fact that they could flash out of the way or move themselves out of range easily, like say if you're trying to grab Cait, she can just net away.
If you want to know how to play vs. a blitz, here are some pointers:
-Blitz is very mana hungry.
-Staying behind minions thwarts many grabs and discourages him from trying.
-Ward the bot bushes that he likes to hide in
-Play a character with an escape (like Ezreal, Caitlyn, Graves, etc)
-Play a character with cc (Taric, Alistar, etc) but not Soraka. Her silence isn't enough and she can't escape.
-Consider taking exhaust or asking your support to take it
-Try not to focus him even if he pulls you. Many Blitz like to take tank runes and masteries.
-Consider building a Banshees Veil late game. It could save your life.
-Play Sivir against him.
-Get your jungler involved. Most Blitz lanes will have you pushed to your turret (don't do this if you're being aggressive and over-extending).
-Don't be aggressive or over-extend. Blitzcrank LOVES to pull you under his turret and knock you up under it, and you may be suffering at least 2 shots of the turret and if your flash is down or you don't have an escape, you can take up to 5 turret shots from this alone depending on where he pulled you.
Hopefully this helps.