Maybe. I have alts and I've never bought a skip potion. The MSQ isn't that hard to get through when you've already done it once. But I wouldn't necessarily say no to them adding that as an option for alts on the same account.
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The main thing I want is to be able to send mail to my other characters, and add them as housing tenants for my plot. But making non consumable mogstation purchases, like outfits and mounts, account wide would be a good start. Some things ARE account wide already so I don't buy that they 'cannot' make more things account wide.
With "better" I mean "more enjoyable" or "more convenient". I'm sure there are people who avoid making alts due to MSQ (me being one of them) which immediately leads to this game having worse replayability for them. All players get what they want if its optional to make MSQ account-wide.
Though, how relevant "Opening Up" the game to these people is, given of all the things you've listed there, the only ones that FFXIV does WELL is Art and the forced Visual Novel.
There are MMO's with much better combat than FFXIV.
There are MMO's with much better dungeons and raids than FFXIV (Heck, WoW's Raids are like the only good thing in the damn game)
There are MMO's with much better crafting than FFXIV.
The only thing that makes FFXIV stand out from other titles, is that it has an absolutely fantastic MSQ.
Now, are there people who don't care about the story and just skip through to go and Craft or Raid? Sure. But it's likely not a particularly large audience.
As for optional skipping of MSQ for alts? Well, MSQ is one of the better ways of actually leveling a class, even if it can take a while to get through.
I mean, your alternative, is spamming Duties ad infinitum. Which is already hard enough stomach on alt jobs (In my opinion). Which personally, leaves me questioning about MSQ being a factor against leveling alts...
Heck, if we could get exp from NG+, I'd be jumping with joy as it would allow for a not so tediously long leveling trip for my alt jobs...
Me personally, I would still play this game just for the combat, art and music. I don't think there are other MMO's out there that provide similar experience in terms of visuals and art when it comes to instances. There's imo really some jaw dropping stuff and I would love for everyone to experience it. Imo it's unfortunate if MSQ keeps players from discovering that, since the more stunning encounters happen at higher levels.
However I might esteem the art/visuals/music more than the average player so my view may not be very relevant. I often play instances for enjoyment even when there's nothing to be gained progression wise.
Define "replayability" then, because I would understand it to mean how enjoyable it is to play the game again from start to finish.
If your alt can immediately jump to the end of the game then, by definition, you are not replaying the game.
It would boost your ability to have multiple characters at endgame, but you wouldn't have to replay anything to get there - except maybe levelling dungeons, but they're a separate element with a question of individual replayability, separate to the game as a whole.
Okay then forget about semantics of "replayability", it doesn't matter. Bottom line is that more people will be making alts. Leveling and playing alts will lead to more gametime, just like how leveling alt jobs on your main leads to more gametime. Having mandatory MSQ for alts will greatly increase amount of time you'd need to progress those chars, but it also probably (greatly) decreases amount of players who will create and play alts, thus resulting in lower overall gametime when taking whole playerbase into account.
With "gametime" I just mean how much time you spend ingame (/playtime). Obviously I'm making assumptions here and even though I'd say they aren't really far fetched, they're still just my assumption and opinion.
There are plenty of people playing multiple jobs. That's FFXIV's primary means of playing alts. Then there are people who do create alt characters in FFXIV. So I don't see a reason to care about overall "gametime" as a player base, especially when Yoshida himself apparently supports people subscribing only when they want to play.