Yep, people don't quite get what that stat actually means.
You're coming from a split pusher point of view but I normally see it from the poke mage vs melee comp or an ADC vs Bruiser. Poke mage will have minimal deaths but high damage and KDA while the melee teammates have lower KDAs and damage. Or you have the ADC being zoned from fight or insta burst so Bruiser does all the damage cause they are alive long enough to do damage.
Poke mages I see boasting a lot when it's not deserves. An Akali is never going to out damage a Lux or Zyra or Brand unless the Akali is literally just diving that ADC/squishy every fight and killing them 20+ times. When your Zyra support is complaining how she carried the game but still lost despite being 8/22 with the highest damage output and no sightstone and then pointing at the mid Akali who went 7/8 and the jungle Warwick who was 3/7 saying mid and jungle lost that for us. No, I'm pretty sure it's that fact the Zyra fed 17 kills to the enemy Eve and refused to ward or stay with the team.
I had a game where my Cho'gath jungle was all "I out damaged our ADC and took more damage than you. Clearly you were not focused in fights. Trash ADC." Apparently being Zed ulted and Hec ulted every teamfight as Ashe means I'm not being focused. And, despite having 2K ish health vs his just shy of 7K (6.8K last I remember) health apparently I'm supposed to out tank him as well since I'm claiming to be focused every fight.
I don't even get the logic behind those two comments. I can't out tank him cause I'd have to die 3ish times to equal just one of his deaths assuming neither him or I am healing during the fight. I'm also an Ashe getting Zed ulted with a 7K HP Cho'gath in front of me. Peel much? Cho literally have two basic abilities that shut Zed down after he ults someone so that his ult is wasted and he used neither to help kill the 22/15 Zed, instead deciding to charge the 6/12 ADC and 4/13 support while Zed and Hec (15/7) kill the rest of the team since no one has the damage or CC to kill them. He's also a 22/5 full tank Cho'gath. KS much? Know what might've helped. Giving some of those kills to our Ekko so he could be full build like the rest of us or letting him take the farm after Cho was full build instead of mindlessly farming waves might've been a good idea too. Cho was also full tank. The only "damage" item he had was Thornmail if you can call it that. I suggested he get Titanic cause he was the only one surviving fights and it would allow him to do more damage. He said I was stupid and my build was aids cause I hadn't got a Last Whisper despite the enemy only having on Frozen Heart at that point in the game.
I did a test in practice mode with the items he had 
and swapped Frozen Heart for 
and only had the base 6 stack from minions cause I didn't know how many he had. I had 5.2K health (with Frozen Heart) and charged up Deadman's. Placed two test dummies in a row and hit them with two auto attacks with both builds (since Titanic is an auto reset you could conceivable do this in a fight). His build, front test dummy took 314 damage and back test dummy took 80. My build, front dummy took 668 damage and back dummy took 482 damage. Took 14 ult stacks to get to 6.7K health with Frozen Heart. Redid the test, same results for his build, my build front took 753 and back took 578.
Yes, you are losing the benefits of Frozen Heart like the Armor and CDR that may have been his reason for buying it. Also with thornmail, it was reflecting 70 damage just from armor alone vs my build reflecting only 50 from armor alone. In addition there is no guarantee that the enemies will stack up like this so that you can get the procs to hit multiple people. However, the CDR only lowered his Q and W by 2 seconds so it's not like that's a big loss to his team fighting and it lowers his ult by 20 seconds max rank. But in 2 auto attacks, I almost tripled his damage output (394 combined vs 1150/1331 combined).
Did another test just autoing naturally for 5 seconds, his: 603, 200; mine: 1341, 1033. Clearly even if you aren't hitting anyone else it's still superior damage if you are using his abilities to slow people down so you can auto attack them down and if you happen to clip someone or multiple people with that Cleave it's going to hurt a lot more than just his normal Vorpal Spikes do since the Cleave passive applies to everyone hit so that's 482 to anyone hit. In addition, this is against test dummies that have 100 Armor and MR. If you do this vs an ADC and/or squishy support and/or mid laner, it's unlikely that they are going to have 100 Armor/MR.
Am I saying you should always build Cho'gath with Titanic? No, but clearly if you are building full tank this might be a good way to get some damage at least with your autos.
