There's a difference between low, too low & underrun heels, which are generally too long but crushed forward. Horses should have low heels and unless they're crushed forward, they're not *generally* too low.
Under run heels, if caused by farriery, is often IME caused from farriers leaving heels too long & 'standing the horse up', which frequently goes along with trimming toes from the ground surface but leaving them stretched forward. Over time this leads to the overlong heels collapsing. Depending on hoof form & the horse's posture, this doesn't necessarily take much. Shoeing long term without respite & consideration about balance, especially before maturity & the hooves have had a chance to grow strong also commonly results in run forward feet with horses who have long, crushed heels & far from recognising what they're seeing, frequently farriers lable these horses as having 'no heel'.
Under run heels, or very low heels esp combined with long stretched forward toes can cause P3 - the major bone within the hoof capsule - to be ground parallel or negative angle(lower heel than toe) on the bottom surface. This puts a lot of strain on ligs & tendons, especially in the navicular region. Crushed, non-functioning heels & lateral cartilages also aren't able to become strong & function properly for weight bearing/impact/shock absorbtion, so this also further inhibits health & strength of the rest of the 'package'. Run forward heels generally go along with run forward toes.
How long does it take to correct? As with everything, it depends. On the horse & length of time it's been going on, how it's treated, the environment & lifestyle/work of the horse, etc. For eg. I've heard so many farriers say they can't be fixed & I've never seen the problem resolved where conventional shoes were used.
I personally feel that shoeing makes treatment a lot harder to address, if not impossible, as it forces the walls to be fully loaded. However, using 'frog support' pads or such, to load and raise the frogs/heels without loading walls can help allow the heel to 'relax back' again & become more upright. This also raises the back of the foot to correct the angle of P3 & relieve unnatural strain from this.