There's nothing special about the bass playing on Metallica's early albums, especially compared to other heavy bands of the time like Maiden. The majority of it was just doubling the guitar riffs, with the occasional simple deviation. There were a lot more influential bass players of the time. Playing bass like a guitar does not make good bass playing. It makes a guitar player who got stuck on bass. Anesthesia is a great example of why it doesn't really work.
I'm not saying he was bad at all, but I don't understand why he's suddenly considered so amazing, aside from the dead factor.