There's many ideas, the real problem is you can only bring 2 summoners, and the game is balanced around bringing Flash.
Heal/Barrier = General Defensive
Cleanse = Niche Defensive
Exhaust = Mixed Offensive/Defensive
Ignite = Offensive
Teleport = Tempo/Mobility
Clarity = Tempo
Ghost = Mobility
Flash = Mobility
Smite = Jungling
Clairvoyance (CV) = Vision
Defensive spells give you a combat effective summoner for keeping yourself alive.
Offensive spells give you a combat effective summoner for killing your opponent.
Mobility spells let you move around the map faster.
Tempo spells allow you to gain combat effectiveness by outlasting your opponent.
Vision spells give you more map control.
Jungling spells let you kill neutral minions easier.
Lets use SURGE and PROMOTE, old summoner spells which were removed, as examples.
SURGE was an offensive summoner spell that gave you a burst or AP and attack speed. The issues with it was unlike Ignite, it didn't guarantee damage in a trade of summoner spells and was easy to disengage from, and came at losing a defensive summoner for an attack speed steroid, which generally wasn't needed on AA carries. Since Ignite dealt true damage, the AP gain required to make most mage spell reels deal that much additional damage would put the few champions who could use it well over the top, meaning it could never have enough of an AP increase for the majority of AP Mages.
SURGE just wasn't going to be used over Ignite/Heal/Barrier without it spawning abuse cases (Say Diana with Surge or some insanity).
PROMOTE was a Tempo spell, very very unique, in that it gave you the ability to push another lane while not being there, forcing someone to go deal with the promoted minion, allowing you to outnumber the other team at an objective to win a fight. Promote was brought back as an item for teams as a tactical buy, since it's main abuse case was in the early game.
Promote gave teams the ability to take objectives too easily when it was up in the early game allowing for too strong of a snowball, making it into an item solved the problems of the spell.
Clarity and Clairvoyance as the unused summoner spells currently.
Clarity because the tempo gain from it is very small and as the game goes on longer becomes less and less, managing mana is fairly easy as costs and itemization are fairly cheap.
Clairvoyance used to see play when vision control was more difficult, but vision is far easier now a days so the map control is far less important.
CV could be removed entirely now a days with no impact on any levels of play. Clarity however is a good crutch to teach newer players and allow them to cast spells to learn how they function as it's usage is simple "Don't have mana, cast clarity." compared to things that require much more learning such as Teleport, Barrier, and Cleanse.