(A pre-note: open-drain is the MOS version of bipolar open-collector. Functionally they are the same: they can only sink current to make a 'low' signal.)
The very first logic families, RTL and DTL, were essentially open-collector. Fun fact: the Apollo Guidance Computer was built entirely from just one type of open-collector RTL IC: a dual 3-input NOR gate. Deeper dive here: http://www.righto.com/2019/09/a-computer-built-from-nor-gates-inside.html
Three-state logic didn’t come until later in the 1960s and early 1970s, with the introduction of TTL with totem-pole drive, and soon after, MOS.
Owing to the influence of those pre-TTL chips, early logic buses didn’t use 3-state capability, instead relying on open-collector drivers for multi-card bus connections and shared signals like interrupts or bus requests.
Ok, so what's good about open-collector? It has the nice property that no two drivers can ‘fight’ each other if they drive at the same time, since OC drivers can only sink current. Also, open-collector makes wire-OR logic width expansion very easy: just connect another open-collector driver to the shared signal.
For computer buses, open-collector has a couple of drawbacks however. The power used to drive a ‘low’ is shed in the pull-up; and the rise time is slow owing to lack of active high-drive. This limits performance.
Because of these drawbacks, and the emerging wide availability of 3-state logic in both TTL and MOS, by the 1980s computer buses (examples: Multibus, ISA bus, NuBus, VME, etc.) had abandoned open collector for timing-critical paths, only keeping it for low-speed sideband signals.
Today, open-collector shows up with some slow buses like I2C and SMBus, where its benefit of non-clashing drivers and known idle state makes implementing a controller network simpler.
Open-collector also allows mixed voltage devices to be used together on the same bus (caveat, with tolerant I/O.) This makes level shifting to higher or lower voltages easier than using push-pull outputs. With open-collector you only need 1 resistor to set the 'high' level.