Seriously? I'd say allow it, there's no reason why an MMO should gate literally everything behind the entire 2.x series story (And probably the 2.x + 3.x story with the 4.x expansions.. And then the 2.x + 3.x + 4.x for the 5.x expansion because that's such a great idea right?)
To the folks saying "The plot says Ishgard doesn't want new people in Ishgard" - The plot of FFXIV is also constructed around the PC being accused of lots of stuff ousting them from Ul'dah. It's literally a plot that only works with one person in mind while playing the game. If "Plot says only those who go through 2.55 can go to Ishgard" The plot says the PC (Read one person) is allowed into Ishgard because that one person was being so helpful from the events of the recent few patches. So, why are multiple people (Read thousands) allowed whenever the plot is meant only for one person? If you're going with "Plot says warrior of light only not Disciple of hand of light!" then you must acknowledge it makes no sense for Ishgard to allow every PC into the game. Maybe make it for someone with a level 50 crafting ability to go through a small quest where you make some high level stuff for Ishgard as a way to allow them into the city, like "Ishgard is in desperate need of more supplies! PC! Make so many of X, Y, and Z, so you can get a work visa and be allowed into the city".
To the folks saying "Crafting is a side thing, this is a combat game!" - Crafting is as important as someone makes it. I know a good bit of people who spend all their time in this game just crafting, or at least just playing the game til they can craft, no grinding for Tomestones or ponies, no daily duty finder roulette, none of that. To them, Combat is just a side thing til they can safely go around and gather their various crafting materials. So, it's important to some people, why not make some dumb excuse to allow DoH/DoL into Ishgard? It's not cheapening your experience.
I can't remember everyone's responses to why they shouldn't do what the OP is suggestion, but still, it's such a bad idea to literally gate everything behind the entire 2.x series of plot with the exception of the new race (And that's one thing that also doesn't make sense in terms of the story). Heck, new players can't even step foot into Ishgard and look at all the new stuff they've got to look forward to. Considering someone payed 40 dollars (In the US anyways) to have access to the content, there's no good reason why they shouldn't at least be allowed to step through the gates. Sure gate story quests behind progressing through the story, that actually makes sense, but not the entire region.