This comes up about once every 2 months tbh.
They used to have a 1v1 mode. Just like a pro 1v1 scrim: first kill, tower, or 100 cs won it. It never became ranked-worthy though.
Basically, people ruin everything: a lot of the people who played 1v1 mode were literally the people who flamed you through your entire ranked game, added you after, and challenged you to attempt to feed their ego (which like 7/10 games ended up backfiring and further tilting the poor ragey kids)
The pros and higher elo youtubers/streamers quickly called it a "cockfest mode" full of those types of players, for good reason.
But as Void and nasu mentioned, there's technical implications to it as well. Mostly, people would play either marksmen, mages, assassins or bruisers, with each sort-of pseudo-countering each other by class. (Ex: ADC > Bruiser, Bruiser > Assassin, Assassin > ADC, and mages sort of varying by exactly what type of mage in what they counter or get rekt by) Supports and Tanks mostly wont have a place, outside of certain "tanks" and "supports" being strong as full AD or AP (which basically makes them bruisers, marksmen, or mages, respectively...and literally anyone who plays a champion with point/click cc already had a huge advantage.