Clarity isn't a spell on Rift anymore so that one doesn't really count. I think that spells are actually not in that bad of a place. There are obligatory ghost and/or flash (unless you're Evelynn or Shaco) for champions but most roles have the freedom to choose their other spell with the exception of the AD and jungler.
Supports go Exhaust (v assassins) or Ignite (v healing teams) for the team utility. Midlaners have the most freedom. Top usually goes TP just because of how isolated it is relative to where the early game objectives are and how well it scales for split pushing (better than ignite.) Considering that the best spell for each player isn't the same for everyone else I think it's fine. The only one that I really think has an issue is Barrier since it seems so underwhelming compared to the rest.
As a note, (not sure how related this is but I was thinking about it the entire time I was typing this) I am one of those people who doesn't like keystones and feels like the old masteries system was more balanced and had more of a skill curve than the current trees. Summoner spells, runes, and masteries are all a relic of older seasons when I think the game might be easier to balance if every champion every game had the same stats as someone else playing the same champion.
- As an example, Anivia can take Thunderlord's, Stormraider's, or Deathfire Touch. She is balanced around Thunderlord's because it is the most popular mastery on her and thus made the other two weaker due to her nerfs across this season. The nerfs due to mastery abuse crowded out diversity. She had hardly been touched prior to keystones and most of her changes had to do with changes to how her ultimate works, bugfixes, and the projectile speed on her autoattacks.
Regarding summoner spells again, EVERY champion is balanced around having access to flash. The examples I mentioned earlier who take neither ghost nor flash as well as those who take ghost are excluded from this. I'm not sure what effect removing flash from the game would do, but I've seen speculation on what would happen if summoner spells were reduced to one option and flash was an innate ability that had a cooldown similar to what it is now. This wouldn't affect most champions, but some such as Olaf, Hecarim, Shaco, and Singed would all suffer due to being locked into having flash over Ghost or another summoner.
I don't think that summoner spells need to be looked at as there are worse problems in the games (keystones.)
TLDR: I am super tired and if anyone actually cares (low probability) I can probably edit and clarify after I've gotten some sleep.