I've stuck with Kha'Zix through leveling to 30 in Season 2, Bronze 5 in Season 3, all the way to my peak at Plat 3 in Season 7, and every change and rework in between. The reason why it has taken me so long to climb is pretty straight forward. I'm not very good at League. I am, however, very good at Kha'Zix. I'd rather learn how to crush any matchup with my champion than learn what champions play the matchup better. As opposed to learning a new mid laner after Kha'Zix was relegated to jungling in preseason 4, I found a way to make Kha'Zix mid work. Fast forward several years and I have bit over one million mastery on this account and about 400,000 on my smurfs. I have no interest in branching out, whether that inhibits me or not. I play to win, absolutely, but I play to win my way.
Since then, I've mastered most top lane matchups to the point of Darius being one of my personal easiest lanes. I actually main mid lane on account of hating jungle in general. Of course, I'm capable of playing that role, as well. Recently, I've started to learn Kha'Zix as a support. It might sound silly, but between Dark Harvest and Duskblade, Kha'Zix has all the damage he needs to assassinate carries into late game and build support/tank items. In combination with evolved W and whatever the hell that allied healing mark is in the Resolve tree, it can be a pretty potent combination in a lot of scenarios. It might seem farfetched, but most of the people who would talk trash about it couldn't even shine the shoes of the platinum ADC mains getting ruined by it.
You want to main Veigar? Even better. Support is the role you'll find yourself pigeon holed into most often when you don't get mid, and Veigar thrives there as well. Stick with it and don't let toxic LCS wannabes ruin your game. If you're honest to God trying to win, then play whatever you want. I'd rather have a Veigar jungle that knows what he's doing with the champion than a bandwagon J4 who just watched some streamer shitstomp and is playing his second game on him. Learn your combos, learn your builds, and if necessary, come up with your own. I don't build boots and get Triforce second item. Do you research and then find out what works for you.
Let me just say that I'm not trying to hype myself up like an asshole. Okay, maybe a little. However, the main point is to demostrate to you that if you dedicate yourself to playing one champion, you will easily crush any flavour of the month bandwagoner equal in skill level to yourself.
Even as Kha'Zix support with one damage item.