Can you make summoner spells work like trinkets?

When you reach level 9, your summoner spells become tier 2 and have a little better stats or lower cooldown. Then you can upgrade your summoner spell to tier 3 with gold, at the shop perhaps, which gives it even better stats? And maybe give it 2 tier 3 upgrades that you can choose from, each gives a new effect to the spell.

Here are some thoughts of mine

Flash: Tier 2: Decreases cooldown to 270 seconds from 300. Tier 3: 1-Decreases cooldown to 240 sec. 2-Decreases cooldown to 180 seconds. Cannot be used if you have taken or dealt damage in the last 3 seconds. (this one can help tanks engage while limiting their escape)

Ignite: Tier 2: Cooldown decreased to 180 seconds. Tier 3: 1-slows the target by 25% 2-Deals 1% of the target's maximum health every second.

Cleanse: Tier 2: Decreases cooldown to 180 seconds. Tier 3: 1- Decreases cooldown to 150 seconds. 2- Makes your champion immune to all cc for 1.5 seconds.

Barrier can give you either better shield or a % reflection to damage recieved.

Heal can either have more heal or better move speed boost.

And so on.

What do you think?