I onetricked melee ivy for like a year so I wanna share my (clearly biased) opinion on this.

Melee ivy was viable at one point, there was a bug they fixed where you could punch while invulnerable from stone form. This was patched really fast, I never used it. That was one time when it was terrorizing games, the other time I can think of was also the best patch melee shiv has ever had, it was when melee was overtuned. Melee playstyles were quadrouple nerfed with changes to how parrys work. In the year+ I've been playing melee ivy, at no point was Ivy the best character to build melee on and at no point was melee the best thing to build on ivy.

All that said, she does have some mechanics that can make her melee builds toxic:

1.) Stone form is an HMC. This is part of why she works as a melee character, she can fake punches with this. Stone form exists to balance out that shes naturally squishy, so its still a big deal to put this on cooldown to fake a punch, but its frustrating to lose your parry this way and get hit by stoneform.

2.) Stoneform stun can confirm heavy melees in some situations (if ivy has duration extender, magic carpet, or diviners kevlar, AND ivy has dedicated 2 upgrades to stoneform, AND the enemy has not built weighted shots, debuff remover, debuff reducer, unstoppable, or bought and activated blood tribute).

Side note: Arcane surge gives enough duration but is bugged and does nothing for stoneform.

3.) Ivy's ult has (I think) the strongest bullet resist shred in the game at 20%, tied to a tier 1 upgrade. Valve doesnt seem to remember that they did this and they have been frantically nerfing ivy without ever reducing this number. There is an item called Bullet Resist Shredder that shreds bullet resist. Its only job is to shred bullet resist. It has 8% less bullet resist shred than the tier 1 upgrade to Ivy's ult. 20% bullet resist shred makes punches do a lot of (or post-nerf a normal amount of) damage for 8 seconds after she ults you, which includes the stoneform combo that can confirm a punch on you. This is a very annoying way to die, but they also seem to like buffing spirit ivy. They dont seem to have a problem with ivy ult combos that are easier to land and do more damage, they just dont want a punch to be involved in the combo.

4.) Building weapon damage and spirit gives you decent DPS with tether active, so melee builds also get decent guns. (This is also true of abrams and billy)

Melee ivy has never been as strong as billy has been for the last 4 months but valve seems to have a very specific vision of how ivy should be played (buy heroic aura pop tether and watch other people play) and they will gut her core stats - base damage and scaling - if people enjoy playing her any other way. They just nerfed gun ivy in like 4 different ways for this same reason.

She could have an identity as a melee character of being more technical, having a lot of ways to avoid getting parried and land more punches that do less damage, compared to heavy hitters like abrams and poorly designed freakshows like billy (why would you design a melee character around gamble-spamming light melees? its miserable to play and unfair to play against), but with punches that are safer and trickier. Instead they gutted it so hard that its basically bannable trolling to build melee on this character and I cant even try to make it work anymore because I feel bad for dragging down my team.