It turns out allowing anyone on the internet to message anyone else on the internet can lead to unintended negative consequences. Who would have guessed?!
To cope with this, many platforms have leaned into a category of interventions roughly described as "consent for messages from unknown senders" - a type of intervention that segregates messages into a construct like a spam folder based on their implicit likelihood of being desired by the user, using affinity checks, user reputation, and other platform specific signals to inform message routing.
At the extreme end, platforms can opt to only allow connected users to message one another - LinkedIn does something like this today, though you can bypass this protection by paying for premium access.
This approach can only be employed in contexts where direct messages between strangers isn't explicitly part of the platform's mission. Omegle could not use an approach like this one. Even so, in perhaps the most open-world platform out there, email clients have found this approach workable (by implementing a spam folder) when used in combination with other heuristics for identifying the likelihood that a user wants to receive a given message.