The idea that “Jack” means “mediocre” rather than “common in the classist sense” is a misunderstanding based on a modern social refusal to acknowledge class structures.
If by "modern" we mean "
no later than the late 18th century, and possibly much earlier," with even the earliest English references often intended to be insulting, then sure. That is, one of the first recorded uses of "jack of all trades" (or, rather, the original Latinized equivalent, "
Johannes fac totum," somewhat literally "Johnny-makes-it-all") was someone speaking ill of Shakespeare because he was both an actor and a playwright. History obviously vindicated Shakespeare, but the point is that the phrase has always had some level of disparagement in it as long as it has existed in English. "Jack" was not just a name used for a common man, it was specifically used for (frequently) lazy, folk-hero characters who won via trickery and luck rather than strength or skill per se. It implied some amount if knavery. And, in the context of the guild system, it further implied having been cast out from (or willingly departing from) an apprenticeship before it finished--either way, implicitly indicating a lack of commitment or effort on "Jack's" part.
It is, ironically, only in the 20th century that you start seeing the mostly-complimentary form, where a generalist is said to sometimes exceed a specialist: "a jack of all trades but master of none/is sometimes better than a master of one." The first half of the couplet is itself a newer derivation (as noted, from the late 18th century), intended to intensify the criticism aspect, as the original "jack of all trades" phrase was too ambiguous for folks who wanted to disparage dabblers. It's also worth noting that there was always a non-disparaging alternative term:
polymath (dating back to the early 17th century, even before the earliest instances of JOAT), which was subsumed by the early 20th century term "renaissance man," its equal for being purely complimentary.
And as far as GPs and such go, most would not see them as a "jack of all trades." They're just as much masters of the medical trade as any other licensed doctor. They just specialize in overall symptom analysis and daily health needs, because that specialty, while seemingly "generic," is actually both very difficult and much needed (most patients don't know what specialist they need; someone who is specialized in determining what specialists others need is thus exceedingly useful.) But even GPs go through the full, thorough process, including a VERY tradesman-like mentorship program (residency) and then licensing by the
guild of doctors national Medical Association. Same with lawyers, who retain much of the old apprenticeship and guild system.
To the other, wholly separate issue: The Jack of All Trades Bard has worked quite well several times, it’s just harder to design well than a simpler more specialized class. In 5e, the Rogue is also a decent generalist, because it has cheats for the action economy. What the Bard (or ideally the Ranger IMO) needs is similar action economy workarounds to allow it to do multiple jobs in a turn.
I'd like to know what these "several" iterations are, because the only two I know of that weren't clearly outclassed (pun intended) within the context of their system are 4e's Bard and 5e's Bard, and the latter is being intentionally excluded from the running.
The ultra old-school Bard was a
specialized franken-build nightmare with no focus (full Druid powers? Mediocre thief skills? 5th level Fighter benefits?)--ultimately just a grab-bag of extra bits stapled onto the Druid chassis. They knew a lot of things and could charm with song, but were otherwise Druids with some Fighter and Rogue benefits. Later edition Bards tried to simplify it and broke things badly, taking away the Druid "focus" (such as it was...) and not replacing it with anything in particular. 3e/3.5e in particular was not kind to Bards, unless they again jumped on the franken-build train (which I have done! It's quite effective...so long as you limit your Bard levels as much as possible while still getting the Bard features you want.)
So...tell me more about these "several times" that the generalist Bard has worked?