I am currently leaning pro-ban.
Alolan Vulpix generally has the speed tier to be able to get veils up safely, but of course isn't overbearing on its own. The main thing veils does is that it renders abusers dramatically more difficult to check, which is most important when it comes to setup sweepers that can threaten to win the game on their own; not only are they immediately threatening, but they also make it much more difficult to get around veils by simply stalling it out. Some of the most prominent veil abusers include Nasty Plot Spritzee, Nasty Plot Vullaby, Shellder, Swords Dance Drilbur, Zigzagoon, Swords Dance/Dragon Dance Corphish, and Scraggy.
Have a look at how their checks change behind veils. Spritzee now avoids 3HKOs from almost everything in the metagame, allowing it to set up multiple Nasty Plots. Vullaby and Rufflet become capable of comfortably 1v1ing every mon in the metagame. In general, OHKOing a mon becomes out of the question; revenge-killing something because you can normally beat it 1v1 is almost impossible, and so veils basically takes soft checks out of the equation. This means that to check something behind veils, you have to wall it (with Brick Break Pawniard being a minor exception). What needs to be considered here is that
a) all of these sets are individually threatening, and there are very few defensive answers that can withstand more than one of them - they easily break generic defensive cores for each other if afforded the opportunity to set up, which veils provides, potentially more than once.
b) their dedicated checks can be very different from each other; finding the role compression needed to check all of them on a single team is a daunting task.
There are two ways to deal with veil abusers:
1. A blanket response to veils. This can be through Brick Break users (usually Pawniard), Defog users (usually Timburr), and fast Taunt users (which, even if they don't shut down Aurora Veil, may be able to prevent a sweeper from setting up).
None of these are terrifically promising. Outside of Pawniard, most Brick Break users both don't want to come in on Vulpix-Alola, and overall find the move to be almost completely suboptimal except for veils. Defog users generally don't actually win against Vulpix-A except for Timburr (and Farfetch'd, which can't safely switch in), who is fairly easy to wear down and takes a good amount from Vulpix-A's attacking moves. Both Brick Break and Defog are a free invitation for certain trappers and abusers to come in; this is essentially a guarantee, without the usual options of doubling or simply using a strong enough offensive attack, because Aurora Veil needs to be removed immediately or other abusers might become unanswerable depending on the matchup. Taunt users are generally unreliable as they don't deal with a target attacking instead of setting up, and Vulpix-A is faster than most Taunt users, so Taunt isn't actually enough to keep Aurora Veil itself off the field.
With that being said, Vulpix-A can be easy to wear down too. These counterplay options may not be reliable, but there's enough so that as long as a team is otherwise sufficiently prepared for the veil abusers, these options should only allow veils to be moderately effective at reducing an abuser's checks instead of massively so.
2. Checking veils directly. Veils makes its abusers drastically more difficult to check, but it doesn't make them completely uncounterable (outside of Vullaby and Rufflet, who suffer from being more easily worn down and revenge-killed than usual). Spritzee still can't break past Ferroseed, Corphish is still walled by Iron Defense Mareanie, and Shellder/Zigzagoon still lose to (Brick Break) Pawniard with some chip.
It's easy to see why this isn't sufficient at all from a teambuilding perspective. Since veils support basically negates soft checks, you have to rely on hard checks. There are a lot of good veil abusers; veils reducing their answers to in many cases just a handful makes it almost impossible to be able to deal with them all, on top of the rest of the metagame that you still have to prepare for. There will always be a veils team with a sweeper that you don't have an answer to.
I'm not comfortable saying that veils teams are broken in the sense that they're too strong. It does skew building to a significant degree - pre-home teams will probably lose to veil teams - but at the same time, it's an entire archetype. Vulpix-A might require more dedicated prep than any other individual mon, even Cutiefly and Vullaby, but unlike Cutiefly and Vullaby, its teammates are quite limited if they want to fully take advantage of its strengths. I do think that an argument for Vulpix-A being broken on the grounds of it being too overcentralizing is available, but I'll leave it be for now.
However, it's probably safe to say that veils is still a top tier strategy. A good veils team is every bit as strong as a good non-veils teams, even when the non-veils teams are broadly and reasonably prepped for veils. This is important because I think veils is banworthy on the grounds of being uncompetitive; veils being a perfectly viable strategy means that it's more akin to, say, SM Baton Pass, than it is to the unviable Swagger in terms of being relevant enough to deal with.
As the tiering policy states:
II.) Uncompetitive - elements that reduce the effect of player choice / interaction on the end result to an extreme degree, such that "more skillful play" is almost always rendered irrelevant.
- This can be matchup related; think the determination that Baton Pass took the battling skill aspect out of the player's hands and made it overwhelmingly a team matchup issue, where even the best moves made each time by a standard team often were not enough.
I wouldn't say veils is quite as effective at forcing uncompetitive matchup fishes as Baton Pass was as it's a lot less versatile, but it certainly does so to a much greater degree than the next biggest culprit we currently have in webs. Web-immune revenge-killers can still revenge-kill a threat; the closest equivalent for veils is Infiltrator, which isn't really a thing because of its distribution. Furthermore, almost every defensive mon that could wall a threat before webs was up can continue to do so after webs is set. Veils actually affects how difficult a mon is to kill, and so reduces defensive checks just as much as it reduces offensive ones. I do not believe that webs forces matchup concerns to a significantly greater degree than other high tier offensive strategies. Of course, this isn't to say that veils is better than webs, as webs has its obvious advantage in only needing to be set once, and so while it reduces the answers for the other mons on Cutiefly's team to a lesser degree than veils does, it's much more consistent and less dependent on matchup to do so.
I claimed earlier that there will always be a veils team with a sweeper that you don't have an answer to, and this is where it comes into play. A veils team will have significant just-win matchups against otherwise solid teams - teams where the opponent lacks checks to the right abusers when afforded the extra setup opportunities from Aurora Veil - and it will have much more than any other available archetype. These might be balanced by various neutral matchups, where the opposing team has the right blanket responses paired with decent checks to create opportunities for playmaking on both sides, as well as negative matchups, where the opposing team has hard checks to all of the veils team's abusers so that overall, the veils team doesn't win more often than non-veils teams. However, I'm arguing on the basis of uncompetitiveness, and I think the number of just-win matchups that veils forces is far beyond any comparably viable archetypes.
Veils creates too many matchups where the opposing side has no real counterplay, and I believe that LC would be better without it.