Not sure if I'm understanding this correctly: It seems like the melee build took a brutal nerf in 1.3. Hit and Run and Fancy Footwork now grant about half the MP, while the minimum AP cost increased by 1, reducing damage output opportunities by nearly a 1/4. In comparison, the reduced damage bonus from skills seems insignificant. Is pure melee build even viable anymore?
In short, yes.
Though it depends on what you mean by "pure melee" and "viable". Melee without using any psi, traps, or grenades has never been practical, and any build that does use them is gonna work fine.
I've played melee builds that didn't include Hit and Run or Fancy Footwork, and only 50% of melee builds use DEX over STR, so those aren't affected by the minimum AP cost changes.
It's a significant nerf for sure, but unless you're on dominating and really wanted to play a non-psi glove or knife build, I wouldn't worry too much about it.
Also, Hit and Run and Fancy Footwork haven't had their movement points halved, they work exactly the same way as before the first time they get activated in a turn. Fancy Footwork can only give 36 MP without specialization, and 55 MP with it. That's obviously worse than before, but that's more MP than Sprint can give, so it's definitely worth taking. Not sure how the rounding works for Hit and Run, so I don't know how much MP it can give per turn, but it's never been as consistent anyway.
Yea, the Contraction tin-can Sledgehammer builds are thriving with 1-turn cd, 0 ap pummel and with LTI also on both Infused Cave Hopper Tabis Sprint and Super Slam cooldown. Other than the Stasis nerfs that hits most of the builds, it's nearly all upside for Sledgehammer stonks imo. Pummel accuracy buffs on low cd is big too. The nerf to Expose Weakness from 50% to 40% isn't that big (read the min INT scaling), and it is possible to skip the feat and not really cry about it. I like to instead slot an Energy Spear with Impale on the off-hand and one-tap to proc Hit and Run at 2-range, and to have the energy damage type available and two different "energy magazines" to skip a battery reload ap cost. You'll miss out on a spiked sledge, but the electroshock generator will often damage-match the empowered super slam anyways as dumb as it sounds (with Psi empathy). The LTI also resets the Impale too which feels great. You also don't need INT 5 if you drop Expose Weakness.
In other news, I really don't think it made sense to nerf the Fists/Unarmed so crazy hard and also leave Firearm Pistols generally untouched other than the (fairly reasonable) moderate light weapons nerf. I know the movement points on punching builds are crazy but they also got nerfed from low-ap attacks by 25% in 4 ap -> 5 ap, Expose Weakness cd nerf, Heavy Punch becoming cooldown-based and Cheap Shots incap nerf. On top of all that is also the light weapons damage nerf and the melee builds vs. +50% increased enemy health "nerf" on Hard and Dominating, melee builds being "feast or famine" due to proximity to enemies means a failure to kill is punished harder. Melee also got hit the hardest from the nerfs to stasis since they would use it aggressively, self-cast to cover their engage. I guess those melee nerfs also hit sledge builds a fair bit too. It's a lot of fist nerfs, but maybe it's not actually that bad? Idk for sure.
I think the biggest winners of the patch are Throwing Knives builds with high INT and full PSI builds with high INT. And obviously also builds that use both of those

. I think a build similar to this with "Pack Rathound" swapped out for "Polymath" being pretty damn cheesy (you can't take PSI feats or Disassemble at level 1, although some other crafting feats are on the table, and also the build is just a placeholder to reference off of):
https://underrail.info/build/?HgMQAwMDCggAwqAAAAAAPEo0Ml8uaDxRY8KgAADCoAAATy8nKz9AFlFcKiFewojChlg-wrNyduKitQLipoYK4qi7A9--Flashbang, LOC mental breakdown with Temporal Distortion damage bonus headband is really fucking cheesy, especially since the pop happens when their turn ends when it awakens them, so you have full freedom to proc Fatal Throw on their stupid heads if they barely survive.
Oh yea and full INT 10 builds with High Technicalities can get doubled spec points if they take "Specialist" at exactly level 16. I don't think any builds other than Laser Pistol or Chem Pistol are particularly stat-min-max'ed for doing that though. Maybe you can make an Energy Knives build op at INT 10 though. I think other INT 10 melee builds will generally just over-kill enemies and have bad ap-target finding economy and are kind of meh. The energy edge on Energy Spears does deal a fuck ton of damage though, so it might one shot sometimes, being fairly decent when it does so against medium health targets. I forgot that fist weapons get an electroshock generator, but I feel like pushing the fist build to INT 10 is a bit of a stretch personally. But I could be wrong.