Since her Chain Finisher gives a huge amount of cooldown to her Standard Skill, if a Skill Haste mod doesn't let Longyan use her Standard Skill an extra time before the Chain Finisher would fully recharge it anyway, then that mod is not useful, as it hasn't allowed her to use her skill an additional time - unless it's worth it to wait a little bit to use her Standard Skill an extra time so you can then instantly recharge it with her Chain Finisher. It usually isn't worth it to do that though.
Skill Haste is theoretically a good stat for Longyan since it could increase the rate at which she can use her Standard Skill, and thus how quickly she generates Tail Flames, and thus how often she can use her ult.
If Longyan can't get enough Skill Haste to get a second Standard Skill in the middle of her chain, then her chain will be
Standard Skill -> shoot 60 shots -> Chain Finisher -> Standard Skill -> shoot 60 shots -> Chain Finisher -> Standard Skill -> ult [This is her default way of playing]
With enough Skill Haste, her ideal chain would be:
Standard Skill -> shoot 30+ shots -> Standard Skill -> shoot <30 shots -> Chain Finisher -> Standard Skill -> shoot ~30 shots -> ult
Since her ult will completely reset both rotations back to the beginning, Skill Haste doesn't let you get more Standard Skills off per rotation - it's 3 for both.
The 1st rotation has 3 Standard Skill casts, two Chain Finishers, and 120 shots.
The 2nd rotation has 3 Standard Skill casts, one Chain Finisher, and 90 shots.
The first rotation gets 10 Tail Flames, wasting the second Tail Flame from the third Standard Skill cast.
The first chain is obviously slower as it has more casts and shots, but it will also deal more damage.
The second chain can have ~90 shots back-to-back with no Chain Finisher, so you'll likely want to manually reload in there somewhere.
Since the first chain doesn't need to manually reload as it does Chain Finishers instead, having to manually reload is a disadvantage to the second chain.
With very good accuracy (and maybe luck) you don't need to manually reload, but in practice you will have to do so every now and then.
Even with three max roll (+19.3) Skill Haste rolls, Longyan can't cleanly do the second chain.
Even after she finishes shooting her shots, her Standard Skill still hasn't quite fully recharged - it still has around 0.5s of cooldown left before it can be used.
Longyan has to stop shooting and just wait for her Standard Skill to finish recharging before she can use it again, probably filling the time with a dodge or two, or possibly a reload.
In practice it'll probably be a reload, as Longyan can have 90 shots back-to-back with no Chain Finisher to reload, so she'll likely want to reload there.
This extra time spent manually reloading is time that the first rotation uses to deal damage instead.
This wait for the Standard Skill to recharge is extremely annoying, and having to stop and wait for her skill to recharge will make the default rotation better simply because it's less infuriating to play, but the wait does make the chain longer, reducing the benefit of doing it.
In addition, this delay is small with three max-roll Skill Haste mods, so with non-max Skill Haste mods, the delay will be even longer, which makes it difficult to swap from the default rotation to the faster Skill Haste-dependent rotation, as you need a lot of Skill Haste in order for the delay to not be prohibitively long.
With a good amount of Skill Haste, it can work, but it's really not any better.
If Longyan is being supported by Tess - Phantasia, then the extra shots in the first rotation do make up for the rotation being slightly longer due to just how much damage Tess adds to Longyan.
If Longyan is not supported by Tess - Phantasia, then the faster second rotation [with the Skill Haste] is slightly better.
Since Phantasia is Longyan's best support, you'll ideally support Longyan with Phantasia, and hence Skill Haste is not what I recommend, but if you have enough of it to be able to use Longyan's Standard Skill more often, then it's not a bad choice.
I don't recommend re-rolling for Skill Haste, but if you get a decent amount of it just from RNG, then you can potentially use it to good effect.
I still recommend you try and get your logistics with +10.0% ATK and either Alignment Index or Crit DMG Amplifier though.