It really depends on the situation. I will use the most infamous turret eater, Yi, as an example. There are a few situations that Yi might view it as more beneficial to splitpush than join up.
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They ALSO have a splitpusher, in which case you would need to send a strong duelist to stop him (pointless sending a Soraka to stop a tryndamere, he'll just kill her and continue pushing.
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The comp is unfavourable for a teamfight. Say the enemy has Alistar, Malphite, Annie, Ashe and Nautilus. CCtopia. Yi is fed but gets deleted in teamfights, too much cc to even wait out. You can say L2play Yi but honestly? It's not easy. It would be far easier for him to splitpush (in which case they need to send 2 or more people to stop him since he's a strong duelist) and YOU need to take advantage of it by raping the remaining members in a 4v3 and shoving all the way on another lane.
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The team score is 10/25. Seriously, everyone on their team is far more fed than yours. WHY THE EFF ARE YOU STILL TRYING TO 5V5??? Splitpushing causes the splitting of forces to deal with the splitter, and that opens a lot of opportunities for one of them to eventually get caught out. Vayne alone at bot because of 4 people chasing the Yi at mid? Why are you wasting time flaming the Yi, go murder her and her turret already!
It's not as clear cut as you think, you could've just avoided the fights in most cases. Defending is easier than sieging most of the time, and you can defend against 5 people with only 4 unless they're massively ahead in which case you SHOULD gamble on the splitpush taking pressure off the rest of you.