It's basically a matter of "how easy is it to understand how to use these summoner spells?"
Clarity, Ghost, and Heal all have clear use cases: Clarity gives you more mana to do things, Heal gives you more health to do things, and Ghost gives you more movement speed to do things.
At level 4, you get Exhaust and Barrier. Barrier has uses similar to Heal, but the uses are a lot stricter and may be harder to understand, while Exhaust also has some well-defined use cases, but has a lot of broad interactions that are not easy for a new player to understand.
At level 6, you get Cleanse and Teleport. Both are really difficult to use properly because Cleanse needs really good timing to use and Teleport needs a level of map awareness that new players won't have. Same with when you get Flash and Clairvoyance at level 8: Flash has too many champion interactions for newer players to understand and new players don't understand the importance of map vision at early levels.
Smite and Ignite are gotten at level 10 for very good reason. Smite is unplayable at anything lower than 10 because of how hard the jungle currently is, so Smite is useless until at least level 10, although the difficulty of the jungle would likely push the role until much closer to at least level 20. Ignite, on the other hand, has a really specific use case that is easy for new players to not understand. Ignite is used to help secure kills, but it is very likely for newer players to use this off cooldown just to deal some damage.
In addition to providing newer players with Summoner spells as they learn the basic skills needed to grasp the uses of these spells, gating the summoner spells like this also prevents new players from getting too overwhelmed by the concept of summoner spells when they first boot up the game. They can learn the basic game mechanics without being overwhelmed by the intricacies of each of the summoner spells.
You mentioned that players already know how to play Mobas would likely prefer to use the high-level summoner spells, but the problem with this argument is that players experience in playing Mobas would level their account up fast enough for the level gating not to matter. In addition, not every single game of a genre is the similar, and Mobas are no different. Even players of other Mobas may have trouble adjusting to League of Legends, so the gating of summoner spells would still be useful as they learn how different League of Legends is from other Mobas.
back there" or "I would have gotten away/the kill, if 
, It has been known that the jungle is best for players who are lvl 30 because they have the rune and mastery slots to help them in the jungle.
