I mean, an enemy disarming every character on the battle map at once is something that makes even the most munchkin of power-gamers nervous.

Disarm is terrifying in 5e. A martial without a weapon is basically already dead, and even if they have a backup it's usually less dangerous.

Picking up or drawing a weapon is a free action it’s not that dangerous so long as one has other weapons or can recover a dropped weapon.

Few martail classes will go into battle with only one weapon. For most if their primary is somehow removed they’d just swap to their javalins and use them as spears.

Hell I always have a spear back up on me in case someone pulls a heat metal spell on me.

drawing a weapon is a free action, but picking an item up off the ground is an action

And if someone stands on the weapon, then it can't even be picked up.

Not true. Under the list of things you can do as part of a movement or action is "Pick up a dropped axe". However, this does mean that the enemy can also just grab it and leave you SOL. Sure you can swap to something like a javelin but then you're looking at at least -1 to damage and losing out on any features you took to bolster your primary weapon.

I dunno about 5e, but when I was playing Hell's Rebels, my cavalier always had a couple of weapons on-hand. Plus she wasn't called the "grapple queen" by the group for nothing.

In 5e when playing martial, I usually try to pick up unarmed fighting proficiency. Its a small chance but you'll never be unarmed at least.

Right up until you fight a barbarian who's convinced that 'disarming' someone means literally removing their arms.

If I was scared of every what-if, I'd take levels of commoner. Besides its hilarious to smite with a bite, kick or haymaker.