For better or worse, in the 00s self-hosting a chat service might have been the least bad option to achieve all the requirements they had. However, it also probably suffered (as I mentioned in another comment) from the fact that many gov't agencies don't really have proper IT staffing and don't treat it as something to continually invest in and maintain/sustain.
But it's more than just NWS Chat:
In December, because of an escalating bandwidth shortage, the Weather Service proposed limiting users to 60 connections per minute on a large number of its websites.
Constituents complained about the quota and, earlier this month, the Weather Service announced it would instead impose a data limit of 120 requests per minute and only on servers hosting model data, beginning April 20.
This is, or should be, bread and butter stuff. The rest of the world has figured out how to do this cheaply and with high availability. And their overseers even recognize this:
Neil Jacobs, former acting head of the National Oceanic Atmospheric Administration, which oversees the Weather Service, said many of the agency’s Internet infrastructure problems are tied to the fact they run on internal hardware rather than through cloud service providers such as Amazon Web Services, Microsoft and Google Cloud.
“I’ve demanded in writing that NWS transition these applications … to our Cloud partners. It’s part of an internal strategy I’ve laid out,” Jacobs, a Trump administration appointee, told the Capital Weather Gang in an email before he left office.
So why are they not making that architectural change?
Because IT is secondary to their primary mission and they don't have a proper dedicated IT team of sufficient size to enable this or a smooth transition if they tried. This is a repeated problem in the federal government. IT is not their mission, and each entity acts like a small-to-medium sized business, even if they're part of a larger scale organization. The US DOD doesn't even have one email system for all services. Each service has its own, and at least until the early 2010s many (most? all?) military bases had their own email servers with military members (and civilians) having to get new email accounts at each new base they worked at (this isn't the case of having a distributed but mutually coordinated system, it was just that each base literally had their own MS Exchange servers running and each maintained them themselves). And that's pretty much the single largest entity in the executive. Now imagine if it was a struggle for them despite a clear mission benefit how much more challenging this is when the smaller agencies are asked to do the same without being provided sufficient personnel and finances to do it, and no leadership (no real leadership) stepping up to create or establish a cross-service solution.
Then NMCI got sold out via contracts that underbid and incrementally removed functionality. Now you can’t recover an account you previously had because they aren’t required to save the account data for more than 90 days (cost cutting) and they don’t recycle addresses due to spillage. Finding anyone without a number attached to their email address has become pretty rare due to that.
Now you have two primary systems in the Navy (OneNet for overseas and NMCI for otherwise) and the USMC has basically broken their network off from the Navy.
Further, each ship has to have its own email servers for fairly obvious reasons.
Kind of rambling, but I’ve worked with that system for a long time now. It’s been interesting going from the legacy military systems, to what was an excellent system, then watching it decay into what it is today.
Sure, they need bespoke computation services for their modeling functions and so forth. But when it comes to the dissemination of information, it seems like that's very much a commodity these days, and can be provided at such an enormous scale at such low prices that it should scarcely be a concern.
I suspect, with no evidence whatsoever, that the NWS is holding this hostage for better funding overall, because it's the visible piece that causes pain to the public. There are other areas where they believe they really need better funding, but haven't been able to convince the budgetmakers of that. In order to force their hand, they're starving the public-facing stuff.