Hmm.. I'm not sure 14 times in the last year and some change counts as "a LOT". Looking at your match history you seem to pick a champ and run with them for a while and go through a lot of different champs. =P That's kind of beside the point, just a reminder that people CAN verify what you say even if it's not that important in this case.
As someone who has something like 45 games as Swain in the last year and who knows how many more (back in my hay day of playing him around 2011 - 2013, I've been an adc main for a while now), I've never had any problems identifying whether or not my ult was on. Let me tell you why.
If you just turned it on, it's on cooldown. So the box is blue. Easy enough
If it is off cooldown, do you hear a horrendously loud "RARRAFGHGHGHLGHGLH CAW CAW SPLOOSH SPLOOSH DOUBLE KILL"? That means it's on.
If it's off, you're dead.
If you're checking your ability bar to see if there is a glowing rim around your ability, you're probably dead as well, and certainly not plotting your next Nevermove like you should be.
Anyway, tl;dr, a new button isn't any more obvious than the cacophony and birds flying around that using your ult causes. What would be super duper sweet and make it very obvious is if there was a screen overlay similar to Rengar when you turn on your ult.. Maybe like a slight darkening + reddening around the edges of the screen above the UI and a very slight greying of the whole field of vision.