So does asymmetry need to be corrected if there is no pain? Probably not in most cases.
I'm not sure if this is a serious question or not but I can try to answer it if you like...
The first thing is that pain is the body's way of telling you that damage is being or has been done - and to do something about it. Whether that's to rest, exercise or get some help in getting it better.
When I see patients, it is usually because they are in pain, but I will examine their whole spine/posture for functional or structural asymmetry which may indicate a deep seated issue which could actually be the true reason for the injury they have. Postural syndromes being the most common I see e.g. "I get shoulder, neck pain and headaches" "Ok, let's check your posture, workstation, muscle imbalances (anterior vs posterior muscle tone, strength etc)."
There is no point treating a problem like this without addressing the cause. The pain might ease, but I can be 99% certain it will return over time without the right ergonomic, postural, stretching and strengthening advice.
In the case of "leg length discrepancy" - it doesn't mean anything unless there's a functional or structural reason behind it. Some structural examples include previous fracture of the femur/leg, hip arthritis, congenital hip defects. These need to be addressed even if there's no actually hip or back pain, because in 10 years time when they are having a hip replacement or have severe disc degeneration on that side thanks to imbalance, they will blame you for not putting a heel lift in or correcting it.
Functional leg length differences are also important - usually due to imbalance or injury to pelvic muscles such as the iliopsoas (which originates from the lower back). Chronic imbalance in this e.g from injury can also contribute to accelerated lumbar disc degeneration through increased tension on that side (some of the muscle fibres actually originate from the outer material of the discs). So addressing it can prevent future issues. They should be reasonably simple to sort out unless it has been going on for a long time, so anyone who says you need 25 treatments is full of shit.
Unfortunately, this is where a lot of specialist areas (in the nhs for example) fall down. They "chase pain" but don't look at how the whole body is affected. Sadly, some people think this is quackery. I see it as proper musculoskeletal healthcare.
A (real) example is that they replace the worn hip joint, but no one has addressed the long term leg length difference on that side before or after surgery. Also no-one has addressed the capsular restrictions or strength of the hip and low back stabilisers. Result = chronic lumbar disc degeneration and eventual prolapse. Once the pain and muscle spasm had been controlled, a simple 1.5" heel lift solved the problem.
So yes it is important - in a lot of cases. But not all.