You buy servers on aws-us-west and aws-us-east, and sync them . How is that very expensive?
There was no accusation of "so easy", only so not expensive and supposedly (and previously, demonstraby) solved in the last 30 years.
They may well be "hard" or even "expensive" for some definition of those two words, but if it weren't, it would defeat much of the (stated/advertised) purpose of outsourcing/cloud.
Geodistributed datacenter requires multiple direct low-latency multigigabit/sec connectivity, special software to manage, test and check it, skilled devops.
Specifically, you risk people piling on that rsync isn't good enough in the modern world and referencing the comment criticizing Dropbox as being little more than an rsync replacement [1].
Of course, the specific tool one uses is irrelevant. The data synchronization problem may not be well solved, but it has been very well studied, with a remarkable number of good-enough options.
So, no, there isn't just one "sync" button, as the parent comment snarkily suggested, but there may be two, one where you might lose the last N seconds of chat (perhaps temporarily) and another where you lose the ability to chat entirely for those N seconds.
[1] Although it had other criticisms, such as monetization, which are, naturally, ignored.
2) Geodistributed datacenters is VERY expensive thing, so not implemented fully.
3) Bad system design, full of "one point of failure".