Splitpushing, why do so many forget about it?

So I was just in a game where the enemy Udyr forgot to take smite so he just afk'd right out of the gates. I reported him as everyone should have, but even though I dominated my lane as Olaf vs a Poppy this was still an insanely hard game.

The issue was my Jinx mainly, we're roughly 15 mins into the game and she's 1/7/0.... my Yi was like 6/8/1, my Diana and Soraka were at least not feeding but they were falling behind in levels due to trying to go and help the other two and just having to run away.

See this is how I understood the situation, it was 4v5, so if they wanted to group and push they would at least be met by 4 others from my team, including a Soraka so all they had to do was not fight and sustain in mid lane. I would splitpush and TP in should any large fights break out or I'd at least pull someone away to stop me from killing loads of towers. It WAS working fine, I killed both top towers, mid tower while they postured around dragon cause they didn't realize it's season 6 and we both already had our first, then I killed the inner bot tower.

The problem was my team for some unknown fucking reason couldn't not fight, Yi would CONSTANTLY jump in on someone, into all 4 of them a couple times, so Soraka would have to try and keep him alive while Diana would typically chase someone away from the fight and the enemy Panth would literally 100-0 Jinx as soon as he saw her in range (which she almost always was cause she kept trying to follow Yi into the fight to kill the low target in the back line). So I'd TP in but all it would do is force the enemy team to run, mine would back off as soon as the enemy did and I'd be left standing there TP-less when I could have been killing an inhib had they not tried to fight AGAIN!

But ofc it was ALL my fault, I wasn't there to engage on the fed as shit enemy team (the Poppy wasn't fed, but Poppy doesn't have to be, but the Panth and Caitlyn were hella fed and even the supp Lux could 100-0 Jinx if she wanted too). They're thinking was "it's 4v5 so let's just ARAM it out in mid lane!" I understand that, but we weren't 20 mins into the game by the time Panth and Cait were ridiculously strong, where both Panth and Lux could 100-0 Jinx through Soraka healing, effectively meaning it would be a 4v4 against a fed as fuck enemy comp in 1 second cause Jinx didn't know how to position. So I splitpush and force the team of 4 to split up even more, I was strong enough to 1v1 all of them, cause Olaf, so they'd either need multiple people to try and chase me down letting my team push up another lane or get another inhib tower since the enemy teams only wave clear was a supp Lux and she was almost required if they wanted to kill me since I had so much armor.

Alas, my team would either fight (not get engaged on.... would do the engaging, I watched it happen 3 times ina row), or the enemy team would send like 3 people to kill me, which took a while each time and I would typically get one of them low, and even though I was only splitting a side lane directly across from my team in mid, they'd use the chance to back off and farm up some more instead of pushing ANYTHING AT ALL!!!! They even left a mid inhib tower they were literally standing directly in front of to go get our 3rd drag.......

Basically even though I had TP I had to sit in mid and baby their bronze asses until I found an opening for a teamfight and pray they'd be able to kill everyone after I killed Cait or at least forced her and one or more others away from my team.... so needless to say this 4v5 took waaaaaaay too fucking long to finish cause my GOLD team was playing ARAM on summoner's rift.....

So if you made it this far, through my fucking novel (I'm actually a writer so I get really wordy, but tend to forgo proper grammar when upset or just on forums, cause how gives a fuck, apologies), was I wrong in trying to splitpush past a fed as fuck enemy team instead of trying to ARAM them in mid lane?