What assumption is hiding behind the decision to adopt such a rule? It is the assumption that the kind of people who like to maintain a back-and-forth sequence of replies with a stranger online are not worth talking to. It's just wasting time. It's not even interesting to the readers. This is a bleak take on the internet, but I'm afraid that this is what online communities inevitably become when people who receive criticism are allowed to return criticism [1]. The only way to stop it is to not take the bait, to never reply to replies. This will not stop other people from jumping into the conversation and start wasting each other's time. At least you're not wasting your own time or energy.
Ego
When someone criticizes us online, the first instinct is to interpret this as an attack, and to return the attack. Why does it feel so important to not let a public attack to oneself stand unanswered? I think it has to do with the kind of "public" we are used to. We are used to small communities where everyone knows everyone and reputation is persistent. Coming out as the loser from a hostile exchange in such a setting can cause a permanent stain on reputation. So the instinct to defend the ego makes sort of sense in pre-urban societies, and also in artificially small communities like schools.
In the online world, where people are more flexible to move around and switch communities, it is less important to keep up one's reputation in a specific community. So even if reputation was persistent within online communities, defending ego would be less important. The thing is, the online communities that work like like school classes are really not worth being part of. They are the bottom trough that capture all the insufferable people from school
Content
Why write anything at all? Why not adopt a rule of never ever contributing stuff online? I wouldn't blame anyone for doing that. But for me, the reason for choosing to contribute something worth reading has to do with a sense of wanting to give back to the parts of the internet that have given me endless entertainment and information. I want online communities to be fun and interesting places. The way to achieve this is not by 'saving' toxic communities by arguing with the arguers [2], but by building new ones with better culture. A sign of a good culture would be that the most honourable thing is to provide succinct, entertaining, and interesting points or counterpoints. Another sign of a good culture would be that the most shameful thing is intellectual dishonesty, and that attitudes below intellectual dishonesty (such as name-calling) do not even appear in conversation, but are blocked by everyone.
Completeness
An additional consequence of adopting the single reply rule is that one has to make entries complete, in the sense that they can't leave obvious room for misinterpretation or misrepresentation. This increases the value to the reader.
An exception
An exception can be made for replies that are well-meant, charitable, and are asking for clarification or more information. Such replies are constructive to the conversation and help build a positive and learning-oriented atmosphere. Note that the exception does not cover replies such as "Great post!" or "Genius comment!", since they are not asking for more information. For such cases, one can use the like button to say thanks. However, it should be noted that indiscriminate positive feedback is just the other side of the coin of indiscriminate negative feedback.
[1] Actually, 'criticism' is a huge euphemism for most of bad faith online exchanges.
[2] The idea of making a community nice by shouting down the trolls sounds so absurd that it's laughable to anyone who has used social media.