Dealing damage is one of the priorities as a carry, yes, but a carry/threat should also be somebody who is strong, if not average, at all 3 periods of the game. Hence why they're labelled as the "carry" of the team; they are supposed to be the strongpoints of the roster.
Turtle is not considered by many a carry because he has multiple points in the game where he's weak. His early game laning and csing has been pretty mediocre since last year. In the mid game, his mechanics make up for it but he's also usually set behind because of his early landing leading to a cs deficit. Of course in the late game, turtle is notorious for being out of position. Turtle fixed some of his positioning issues for playoffs but it's clear that the problem is still present as evident in games 3 and 4 against Liquid. Other than that, his early game and laning are still pretty bad imo, though it might just be TSM's early game as a whole, and it's shown in their series vs Liquid.
Those damage numbers that you brought up are fancy and all but you have to consider a few things:
Turtle was playing kog'maw, one of the highest dps adcs in the game.
The series where you took the data from was one that was biased towards turtle in a way since he was the only member of TSM that didn't shit the bed.
Similar to my last point, bjergsen, TSM's main damage dealer, didn't perform optimally meaning that turtle, being the adc player would most definitely have the most damage done in all game. Bjergsen was also playing yasuo for 2 of the 3 games meaning that turtle has more opportunity to do damage as kogwith the increased range and poke from spells whereas bjergsen on yasuo has to go into melee range.
Turtle performed well in the semis, yes, but it's important to note that in those games, bjergsen did a lot more damage than turtle. Bjerg was the main damage dealer in the series but turtle was the executor who finished them off with his jinx ults; precisely the way that he got ahead in the first place. Accurate jinx ults that finished off chunked Liquid members in skirmishes.
It's not that turtle isn't "carry" for TSM, it's that he's aalso a liability for a good portion of the game and in order to get him to stay even or to get him ahead, TSM has to allocate much resources such as farm and kills in his direction. Turtle obviously isn't a bad a, hence why I said that his mechanics are great but his game sense and positioning need to improve. There's obviously something that caused him to drop off from being a top 2 NA adc from 2013 to 2014 spring till now, an average adc. Maybe it's communication issues with lustboy? Who knows?
To address your point about dyrus, solo queue =/= competitive. The soloq top laners are nowhere near as good as the top laners in the lcs. If Dyrus can play all of the carry champs then why isn't he picking them in the lcs? You can't really argue that the team wants him on tanks all the time when throughout the course of the WHOLE SEASON, it's been shown that triple threat teams are the most successful. FNC, SKT, LGD, EDG, KTR, CLG, IG, these teams some of the best from their regions and all of them usually run comps where there are 3 damage threats. How could dyrus become a damage threat when he's always put on gnar, maokai, or shen, when olaf is banned. Why isn't he put on a yasuo, fizz, rumble, or hecarim? It's either dyrus isnt confident enough in his ability to play carry top lane, or, regi, loco, and the rest of the TSM coaching staff has failed to see what has been successful all year round.