It wasn't really a replacement - Ethernet was never tied to specific media, and various cabling standards coexisted for a long time. For about a decade you had 10baseT, 10base2, 10base5 and 10baseF deployments in parallel.
I guess when you mention coax you're thinking about 10base2 - the thin black cables with T-pieces end terminator plugs common in home setups - which only arrived shortly before 10baseT. The first commercially available cabling was 10base5 - those thick yellow cables you'd attach a system to with AUI transceivers. Which still were around as backbone cables in some places until the early 00s.
The really big change in network infrastructure was the introduction of switches instead of hubs - before that you had a collision domain spanning the complete network, now the collision domain was reduced to two devices. Which improved responsiveness of loaded networks to the point where many started switching over from token ring - which in later years also commonly was run over twisted pair, so in many cases switching was possible without touching the cables.
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