AFAIK Zombine behavior, canon-wise, is explained (more like “attempted to be explained” though, since they’re primarily a gimmick and nothing more) by certain biological functions being embedded in Combine’s neural system through chips and prosthetic and whatnot.
Zombines have also been observed to communicate over radio, but in a highly limited manner. There’s a reason why only zombified Combine do these more-or-less advanced functions and no other zombie does - it’s unique to the Combine’s biology, more specifically, neurology. Zombines have been observed to lack brain in its entirety, by the way.
If HECU zombie can unholster a grenade and pull the pin out while holding, and that’s quite some motor function for a zombie, then why shouldn’t they be able to swim, climb, run, or even shoot weapons or something?
And from gameplay perspective - that would probably change a lot and make it played more like HL2 than HL1. For example, one of the things you can do with a Zombine in HL2 is steal its nade whilst he’s attempting to kill you with it and then throw it back at him or away with gravity gun - but there’s no gravity gun in HL1 and BMS. Zombines aren’t really favorites of anyone’s either, they’re generally avoided in campaign mods.
*NOTE when I speak of “HL2” I also refer to “EP1” and “EP”.
It is worth noting that just like many things in the Half-Life franchise, Zombines are more of a gimmick and gameplay element, and then story/canon is coined around that. That’s primary reason why a lot of people prefer HL1 (that includes BMS and HL:S) over HL2 - it didn’t try so hard to have some meaningful story, you were an any-guy, hence why you never spoke, you felt like you were making the decisions, not Gordon Freeman. And then suddenly in HL2 there’s this attempt at going deep in trying to explain everything, but at the same time leaving so many holes, so many things just unerdetailed - that’s why the HL franchise is so infamous for retcons and numerous post-factum changes by writers. So, yeah, let’s stick to what works, all right?