I think the main issue is you're conflating a parse run and a speed run. You use both terms, but you seem to use them synonymously. A parse run is meant to feed a single individual's damage to get their damage up as high as it can go, oftentimes beyond what that job's actual limits are because of just how hard they've been fed. With this in mind, you can take any job in for a parse run, within the constraint that the party has to synergize well enough to be able to feed (so, more often than not parse running a non-meta job will mean you're going 7/8 speedkill meta). Even when doing parse runs with the full speedkill meta, you're going to prioritize one member over others more often than not because feeding is important for parse runs.
So let's answer this question: why would you take a non-meta job into a parse run? Admittedly, the biggest reason I can think of, and what my static's White Mage did, was find a group outside of our static that already got their clears for the week as well, and take turns doing parse runs where they optimized the strategy and synergy around making sure he got the highest parse he could.
All this to say...this weird narrative that White Mages cannot optimize is definitely weird. You might as well say that SAM and BLM were fine, their damage was high enough it's just you couldn't optimize with them like you could other DPS and all the good DPS went meta anyway so the results are skewed.
inb4 "I know that I'm orange in every fight and you don't even play healer"
You asked "Why would anyone take a job that takes away raid dps in a parse run or speed run?" To answer that, I needed to define my terms clearly. Speedkills will naturally get high number outputs because the boss is dying at ludicrous speed; therefore, you would of course go full speedkill meta to try and achieve speedkills because the meta offers the greatest raid DPS, and thus, the fastest kill. Parse runs are about feeding, not speed, although speed can and does matter, it's not the priority.
I guess it could be crystallized as speedkills care about total rDPS, while parse runs care only about the player's individual pDPS.