League had two different split push items, and both had to be removed/reworked because they were unhealthy. One gave lifesteal and armour pen, then attack speed when versus one or less enemies, which led to a handful of champions like trundle/tryndamere/sion being able to delete any tower in two seconds if ignored and 1v1 anyone with just basic autos due to the amount of stats it gave them. So either you ignored them and lost every tower in a lane in about 30 seconds, or you send 2/3 people to deal with them and then the rest of their team wins the 4v2.
The second item made minions have extra armour/magic resist, and used to give the owner bonus armour/magic resist when not near allies, which made certain tanks almost unkillable if they were solo, which was eventually changed to a 4 hit passive that dealt bonus damage to towers and it doesn't get built anymore.
The problem is either you have an item which is only okay in a 1v1 situation but does nothing in teamfights, so maybe gets built on a splitpusher once every few games and is largely ignored, or you have an item which is okay in teamfights and then completely busted in the 1v1 situation, so any time a splitpusher buys it you're forced to send 2-3 people to have a chance at winning the fight, leaving the rest of the map wide open for their team. Or you just get every splitpusher forced to build it into their opponent building it which severely limits build variety.