Apparently Valve experimented with melee weapons early in development, but intentionally decided to cut them because of the perceived lack of impact and weightlessness of held items, but the main thing was that playtesters kept getting their long melee weapons snagged on stuff. Alyx notably does not allow your hands or held items to intersect with other objects, nor does it let your hands get too far away from your body’s position to prevent shenanigans. If you unexpectedly hook your crowbar on a door frame or a table or something you’ll find yourself inexplicably leashed to it after walking a couple of feet and then not be able to find your hands.

This article goes into some detail. Apparently the crowbar specifically was removed to prevent players from assuming they were Gordon Freeman, despite the constant stream of evidence to the contrary. But it doesn’t seem like too much of a leap to replace that with Alyx grabbing a random length of pipe or chunk of rebar or something from the multitudes of trashed urban environments she traverses throughout the game.

Anyway, as soon as modding support was opened up for HL:A the first things that inevitably appeared were about 4,987 mods that added the crowbar back in. So it’s an easy enough wish to fulfill, if that’s what you want.