RCA weren't designed to carry much current. They're typically used as a low voltage connector for line level signals. They're also known as Phono connectors because they were originally invented by the RCA corporation of America as a way to connect the low voltage signal from a cartridge on a phonograph to an amplifier. That might tell you quite a bit about the voltages expected. A moving magnet cartridge puts out around 0.003 Volts and no appreciable current.
My understanding was it was originally of European origin and possibly by the Cinch manufacturer, as an RF connector but with a shorter pin than we are accustomed to [similar to the Belling Lee coax plug] and quite fiddly to get into position to insert, RCA realised this and started manufacturing plugs with a longer pin to make them easier to mate and gave it the RCA title, I believe this was for use in their transmitters.In those days a magnetic cartridge connector would often have been what we now call 2mm banana plugs.
We use RCA connectors for other line level signal connections such as CD players where the voltage is higher: 2-3 V. But again there's no appreciable current.
Although not designed for it, a decent RCA connector will carry around 2 amps of current and has sufficient isolation to carry 300 Volts. I wouldn't recommend it as a safe connector though. Luckily, the 4 Ohm speaker with a 20 Watt rating won't carry anything like that voltage, but in theory it could carry more current.
The power equations for a 20W speaker at 4 Ohms give us a current of just under 2.25 A. This presumes of course that the amp in the active speaker can deliver 20W, and that you might have the volume control set to maximum. In all likelihood you'd listen at lower volumes and so the current would be less in typical use.
Whilst it's not the original intended design for RCA connections, I have seen home cinema kits use them as a connection for speakers. But here's the thing; the speaker-end connection either had a matching RCA or the wires went directly in to the speaker and so were hard wired. I haven't ever seen an RCA to either bare speaker wire or banana plugs. That doesn't mean to say that a Heath Robinson connection like it couldn't be put together, but it's definitely one of the more unusual concoctions.
The safest thing to do here would be to see a picture of the sub plate amp on the back of the active speaker. This would confirm that an RCA socket is used for the speaker level output to the passive speaker.
Have I missed something to do with a sub of some sort? I haven't seen mention which is why I've asked. My interpretation so far has been for PC speakers, as pictured, which
in my experience only use 3.5mm jack or phono connectors even for the active PC amps purporting to be 225w per channel, yes I suspect they really are only low power devices with a manufacturers wacky method of measuring.
If these are on a 5.1 system or similar then yes I'll agree phono plugs are extremely common for the speaker connexions as Lucid describes. Indeed phono connectors were also quit rife in the 70's hifi boom for loudspeakers although not as popular as 2p DIN, banana or screw terminals.
I think it was Trio [certainly one of the early Asian makes] who used to use them on their 100W HF tranceivers which IIRC didn't cause any problems. They were still used until fairly recently, and possibly may still be, inside radio equipment between stages with the original short pin, often running at 50W [@50ohns] of RF continuous power. They were also popular in aerial distributuion systems along with a locking ring version of Belling Lee until F types took over. They are not the delicate product you seem to indicate.
Having said this phono plugs of either variant would not be my first choice for anything other than hifi systems.
Lastly I don't understand why you describe a particular lead style as Heath Roninson concoction when it used to be freely available in a bubble pack hanging on a rack in every single hifi shop.