OSS did not have the ability when it was removed from the kernel and replaced by ALSA, which did have that ability already.
There were (and are) many problems with the OSS API, a number of which continue to exist in the ALSA API too.
All serious audio APIs (plugins, or native audio I/O) use a pull model at the bottom of the stack, so that i/o is driven by the hardware. You can layer a push model (where software does blocking read/write calls whenever it wants) on top of that, but not the other way around.
And yes, OSS and ALSA both implement select/poll etc. for audio devices, but do not enforce the use of this model, resulting in the 2000s being filled with Linux (and *BSD) apps that couldn't function correctly without oodles of buffering.