I'd say the most vocal of the players who harass others in PVP for being new are the minority except in the case of The Feast. Ranked solo queue honestly brought out the worst in the community due to the huge detriment of having a new player on your team. Being new to Frontlines is usually not met with hostility and a new player in 8v8 wasn't often met with hostility.
So your point about needing something to inform players of PVP and a mode with nothing at stake needing to exist is definitely true. Unfortunately the queue for 8v8 feast couldn't be sustained and there was no real 4v4 practice mode. In fact there's pretty much no way currently to practice PVP without just jumping into a queue and trying your best. which is of course part of the problem.
As for how our community has a toxic reputation while also not really being that toxic. First off this isn't directly due wholly to FFXIV. This is a problem that has manifested over the years throughout any form of competitive play(and even casual play) involving western players in any game. You can look at the standards for PvE content and see how often people have freaked out about having a bonus, or new player who hasn't watched a video, etc. to see where part of that fear can come from.
Players think something like "If I get yelled at in PvE for missing a mechanic, what will happen in PvP where the fights aren't scripted?"
Then we have other PvP outside this game such as League of Legends, Call of Duty, World of Warcraft,etc. where the community can reach and absurdly toxic level. In these days plenty of people have seen games like this played or played them before themselves and the think "Every time I go against players people show their worst sides. I'd rather just not PvP in any game. If anything i'll watch someone else PvP."
Then to lend credit to this reputation of toxicity the ones who are the loudest wind up being the rudest as well. I myself rarely ever talk in PvP and I don't mind helping others, supposing I have the time to do so.
By time I mean that at least in the most recent competitive mode I really didn't have much time to explain to someone everything they need to know when coming into the feast solo queue. Then when situations like that arise most vets will go "Ugh, a new player? We lost. This sucks, why would you come into ranked, why don't you already know the rules?"
Then to further the frustration, and I hate to be that guy to say this but. The FFXIV community is probably the least skillful community as a whole I've ever played with in any game. I suppose the difficulty curve of PvE being low is partly to blame. But getting a new healer for example wouldn't as big of a detriment if they actually knew how to heal in the first place. While yes PvP is different than playing the PvE portion of the game there's no excuse for a Scholar for example where the only healing going out is Embrace, that wouldn't even cut it in hard PvE content, yet these are the types of new player you're most likely to see.
So the problem is a big one partially due to the design choices of FFXIV, and partially due to the overall reputation of the western community not just in FFXIV but in other games as well.
Unfortunately without something keeping older modes alive every time a new season comes out the level of toxic players will also rise, and the amount of new pvpers coming in will also decrease.
It's a terrible situation and the one way I can think to fix it is for them to start doing official tournaments, streaming matches for spectators, etc. However before they can even attempt that they'll have to learn how to properly balance PvP, and frankly they just are very bad at it.
Apologize lol. Super wall of text, I type too much sometimes xD;