I'm not sure Discovery can create time travel to alter the Cage.
TOS already altered "The Cage," when "The Menagerie" repurposed footage from the end of "The Cage" showing Vina going back underground with an illusion of Pike to represent Pike's actual return to the planet 13 years later. It also altered the pitch the Keeper's voice. This is fiction, after all, a creative work, and alteration is part of how creativity happens. The way something was originally intended is not an immutable absolute, because it's all just stories, and it's the nature of stories to get changed in the retelling.
Except not everyone at Trek is the best at everything. Picard got the Enterprise at nearly 60.
Huh? He got the
Enterprise because he was the best -- because he was
already a legendary captain from his 22-year tour in command of the
Stargazer. Roddenberry basically recycled TNG's cast from the abortive
Phase II revival -- Decker and Ilia became Riker and Troi, Xon became Data, and the older, seasoned veteran Kirk became Picard. The idea was that Picard was the legendary older captain serving as the mentor to the up-and-coming Riker, who was intended to be the action lead in the Kirk mold.
Which has nothing to do with whether he was the best, because "fastest" rarely means "best" in anything outside of racing. Experience is what makes a good captain, usually.
Sisko was a burnt out officer given DS9 to shake up his spirits.
Or rather, because DS9 was expected to be a post of relatively low importance, until the wormhole was discovered.
Is there someone on Twitter we can politely ask why the writers decided to amp up Pike's age to match Georgiou's?
That seems self-evident to me -- because they wanted to establish a history between Pike and Georgiou so that he'd get suspicious about her changes in behavior. Besides, Pike's age was already retconned a decade ago in the movie. He was old enough to have been born before the timeline split, therefore he'd be the same age in both timelines.