Should Flash Be Removed/Changed? [Video + Suggestions]

In this video, "Necrit" points out the negative aspects of flash, and asks the following question: Should flash be removed? I wanted to put this up for debate, as well as propose a solution to what seems to annoy players like Necrit.

[Necrit's opinion summarised] When Riot introduced summoner spells, they introduced a pretty wide variety of unique spells. They were aimed at making the game more flexible, so that players could play their champions however they wanted. However with time, some of these spells predominated the others, namely : flash, ignite, and teleport. (He doesn't mention smite because of its particular role in the game) Because these spells are available to everyone, using these spells kind of goes back and forth. Flashing in for the kill, enemy flashes out as well. Some might think this is not too much of a problem, but low mobility champions such as Kog'Maw have a very difficult time dealing with flash engages, even if the player has flash himself, the escape potential gained for Kog'Maw in outweighed by the opposing champion's chase potential. Many champions that rely on summoner spells to be viable have therefore a reduced skillcap.

His solution is the REMOVAL of flash.

[My idea for a solution] A potential solution would be a nerf to Flash's cooldown, but with a twist. I believe that if Flash's cooldown was increased significantly by default and remain that way throughout the game, the same problem would occur with champions dependant on Flash to do well. Instead of giving Flash a flat nerf, a possible alternative would be to increase general cooldown, but have it reduce as live games go on. The cooldown of flash could be determined my the game's average champion level or simply by time. Side note: I think having Flash scale with individual champion level is not necessarily a bad idea but would require careful balancing to avoid snowballing.