Gunlines vs. Melee - how should PP think about this?

Good question. In theory you want it set up so that all other things being equal a gunline vs. melee centric army should be a roughly 50/50 proposition. Gauging how many melee dudes need to get through though is tough since I think the answer, even among gunlines, is going to vary depending on the rest of the list composition.

Then you also want to factor in that the mixed lists (i.e. mix of melee and gunline) should also, in theory, be able to win 50/50.

Interesting subject for debate.
But may I ask which gunlines you are referring to?

Besides the occational Cygnar player who drops his gunline list I pretty much never see shooting in my local meta or regional tourney.

Imo Melee wins hands down.

I think SR17 and now SR18 has done a fair amount to counter gunlines, I don't know if there is much more need for explicit anti-gunline tech baked into theme force benefits

In my opinion the whole shooting thing in wargames can be generalized and lumped together with things like Sprint (to a certain extent and by concept, not how sprint currently actually works). Shooting allows for big gains with 0 risk, as does some absurd yoyoing (which I think is not currently possible maybe outside Kaya1, if even there?) -> hit the target, run to safety without the chance of retaliation.

This is problematic design, because EVERY player will do that, and choosing targets is often not hard at all. Everyone will take free gain with no risk, so these kind of situations are not very interesting game-wise. Currently PP combats this (in addition to things mentioned) by having bad(ish) guns (and those said themes, for example), meaning guns rarely take out the opposing force before it can reach you. The solutions are not elegant.

To improve the situation (if one wants to do that)? There are number of things, used in wargames already; Make shooting more interactive, alternate activations, increase the amount of terrain, make shooting somehow more risky (allowing some increase for the power) - not maybe usable in warmachine, but due to my lack of imagination; malfunction - or remove most of the shooting from the game and keep it a special case.

I don't think it unlocked Nightmare, seeing as he basically already has Stealth and Ghostly, negating the need for Carapace. Nightmare is still really expensive. Though I would argue that it did unlock all the bipedal warjacks (except indeed the Inflictor, its role didn't really change), in a way that Infernal Machines never could (it was a poor excuse for a jack theme because they wanted to give us something while they worked on BI). ARM 17 is just really low and while DEF 13 is quite nice (doesn't go for Seethers), most things that are good at their jobs have MAT/RAT 6/7 and coupled with the low ARM can still take out some systems. Shooting off arms has always been a weakness of Cryx bi-pedal jacks, so Carapace was the logical path to take, though I agree it probably shouldn't affect free strikes.
I would argue that it also helped crab jacks to make a viable gun line without getting shot too hard in return. Though this is of a lesser impact.

I honestly think this was a great solution and it made Cryx jacks see table time. Look at the WTC lists and you will find that heavies are still only taken to fill out WJ points in anything but Black Industries and there is good reason for that: it's very hard to get mileage out of them without the ability to spam and/or keep them safeish on the approach (Goreshade 1 also helps here, but he's not very popular).

The problem arguably lies with Asphyxious 3 in that he shores up the melee weakness as well, while making them all fast and gain Pathfinder. Lists with other casters like Venethrax or Denny 2 still really feel the ARM 17 and get crushed if they get out-alpha'd. Although, like someone else said, dedicated combined arms or infantry based melee lists can still easily take out Slayers, even with Carapace, and Slayers still struggle to take on real opposing heavy bricks.

EDIT and actually on topic:
I feel like at the moment ranged is still quite viable, though it's currently mostly in Cygnar and Winds of Death? Others can do it, but they are not very popular for a variety of reasons. Gunlines are still very strong into infantry spam lists and combined arms list can benefit from having a shooting units available, such as Idrians in a Magnus 2 list. They serve their role and usually get in a turn or 2, sometimes more, of good shooting before being overwhelmed, which I think is reasonable.
Actual dedicated gunlines like Rasheth, Siege 1, Nemo 3 (though nerfed), etc. can still be devastating at range and can inflict so much damage that, after the lines close, they can often get by with their more limited melee capabilities. They also often have elements to help with this, such as tortoises in Winds and Striders/colossals in Cygnar.
Have such great spot removal can also be very useful on scenario, while the scenario still forces you not to simply stand and shoot, creating more interaction for the opponent.

There are indeed lists out there that prey on full gunlines (and even then, can still get overpowered in some cases), but that is the case for every "skew" in the game; there will be hard counters out there, so you should cover that with your other list.

TL;DR: Gunlines still have a place in a competitive pairing, you just can't put all your eggs in that basket because it's too likely to be hard countered. And I think that's a good thing for the meta.