I shall explain the reasoning behind the level restriction:
Smite: Have you ever tried to jungle with 10 masteries and tier 1 runes? I never did on my main account because I never understood the jungle concept. But once I understood the game, I made a second account to play with a friend. Short story. Once I got the level for smite, I tried to jungle.
You just can't/it's really hard and annoying. The level restriction is to avoid people trying to jungle at super low level and get executed without any chance to survive.
It's to force you to concentrate on certain aspect before doing the other one.
But even if I understand the reasoning behind every level restriction like
TP: Gank/Map pressure tool. Even people in silver sometimes don't use tp correctly. The number of minion TP near their turret I saw is insane xD. (cooldown is lower if TP on tower)
Flash: Super versatile. Can juke/Avoid skillshot/Save distance/Create distance and so many more. Someone still trying to understand the concept of CS, poking, trade, itemisation and jungling (which is harder than it used to be because of the smite buff) will just lose himself. So they keep simple spell at low level.
Clarity: Speaking of simple spell. That's the official new player friendly spell. If you remember your noob time like me. You probably remember your horrible mana management/spamming spell on minions.
But I agree on one thing. Since Flash. TP. And jungling are mechanics you will ALWAYS use. To make new player use them later is counter productive. And duo lane are something discouraged because you win less XP/split CS and new player will probably don't have knowledge of these thing.
TL:DR There's a reasoning behind the spell level. But Riot might want to re think them/fix the god damn tutorial, since this reasoning is counter productive. Honestly, if you don't have any friend playing this game. You'll never understand correctly how to play because smurf rather be like:
"noob omg you are bad why can't you do the lcs big plays even if you play only since yesterday omfg thrash team" than actually helping them to understand.