Lots of elite prep schools in the US use a similar system, for similar reasons.
Yes, there are people who have trouble with public speaking to a debilitating degree, but it would be excessively rare for someone to not at the very least in a one on one with their professor/teacher be able to be so badly affected as to not seem they've even heard of a topic or at least be able to prove they've worked on it to a certain degree.
I would be immediately skeptical of any student who claims they are completely unable to explain their knowledge unless they are allowed to work in complete isolation with nobody to monitor they aren't cheating in some way.
I think the hard answer is that to some extent you just have to learn to. I mean, you could sit silently in supervisions if you really insisted, but to participate properly you just needed to build the confidence.
Is it fun? No, but it's a pretty accurate reflection of life after school: nobody in the real world gives you points for "couldn't say the right thing at the right time, but was thinking it"
Those of you who severely lack any of the three will be penalized. Just like someone who can discuss a topic orally but could not write it up would be penalized.
Of course the current setup works badly for those who explain it much better by speaking.
Can you communicate it in real-time through writing? Maybe that's an accommodation that could be done?