Making Ignite a true, relevant niche summoner spell
TL;DR: Removing Grievous Wounds from summoner Ignite and adding a new, more powerful passive will solidify Ignite as a summoner spell with strategic use, rather than something that is simply used to add a few extra ticks of damage. (I highly recommend reading the whole explanation, but feel free to read just the proposed change in the mid-section)
Personally, I'm frustrated about the state of ignite; it's not terrible by any stretch, but with the changes to grievous wounds, every time you're against a healer it feels really underwhelming. Being a summoner spell with a fairly long cooldown, it makes sense to me that the healing reduction it applies should be more powerful than an item you can simply purchase. This would allow you to decide whether you want to take ignite, and really cut down on enemy healing during a very short window, or take a different summoner and build into a more consistent (but less effective) form of healing reduction. So I think Ignite should have a passive different from grievous wounds called "mortal wounds"
Mortal Wounds: Healing from all sources is reduced by 60%, shielded units take double (maybe 1.5x?) damage from ignite for the duration of the shield (numbers could potentially be adjusted) IN ADDITION to this passive change, the cool down of summoner Ignite would be increased from 210 seconds (3.5 minutes) to 240 seconds (4 minutes).
The goal behind these changes would be to solidify ignite into the niche it used to occupy, where you were attempting to completely shut down an enemy and kill them during that 5 second window. While I think it would be neat to add some sort of overall damage amplification (think like a lesser DFG) doing so with what ignite already does is both outside its core fantasy and completely overpowered. The addition of double effectiveness against shielded targets (and this would have to be hp shields only, not conditional shields like Morgana's Black Shield, or any spell shields such as from Nocturne, Sivir, or Banshee's) would be to have ignite actually be a useful summoner spell against champions who would otherwise simply shield themselves and continue to fight. It won't completely negate shields, and if you want to truly be effective it's still better to wait out summoners like Barrier, but it significantly cuts down on shield effectiveness such that if you are able and willing to wait a few seconds, their shields will be down and they will be vulnerable. This is a fairly significant addition of power to Ignite, and as such the cooldown was increased to somewhat balance out for the increased effectiveness against shields and heals. By having a 240 second cooldown, it ensures that (before masteries) you will always have your heal or barrier to help combat the enemy's summoner ignite, and it simply becomes a matter of chicken between the two of you in a 1v1, where they can ignite early and you can wait it out, or you can try to heal before ignite reduces its power.