I suspect that some of this is tradition because there are small solid state amplifiers. I'm surprised no one has made a small receiver for 2.1 system cause would be pretty common.
They do make half size receivers, but they typically only have half the power output. The space savings comes from removing space for airflow and the heatsink, and using smaller capacitors for less heat and smaller power output.
If you only need 2.1 output and a quarter of the power, there are offerings that are basically the size of the minimum amount of ports: 2 pairs of speaker terminals, a pair of RCA terminals for subwoofer out, a HDMI port, a optical port, and power. But then it's not really a receiver and more just of an amplifier+DAC because they only have one HDMI input/output, having space for multiple HDMI ports or speaker terminals basically increases the size to the offering above.
They're big mostly because consumers demand a lot of big connectors on them.
Sometimes I see cheap "amplifier only" designs that are about the size of a small 2U rackmount, but then you usually give up a lot of inputs and controls; they seem to be used either as PA amplifiers or as "extra room" units in the weird whole-house audio systems that apparently thousands of people had at one point and all dumped in the Goodwill.
If your speakers are active and don't need an amp, you can use a HDMI audio extractor, those are pretty small (mine is about half the size of my phone)
