I believe Grok is already as deeply integrated into the gov as can be, but it's objectively the least capable model family behind OpenAI, Anthropic, Gemini.
So the Gov could very well rely on it alone, purely on ideological grounds, but then they'd be condemned to using inferior tech at a time when everyone is really nervous about staying ahead in AI usage (rightly or wrongly). Not sure they'd be willing to accept that, and it does put pressure on them.