As someone who actually works in government, here's the deal:
First, people who work at home do actually get a lot done. Everyone is different, whether they're students in school, or people working in an office - some work better around others, others work better on their own.
Second, the long wait-time isn't because bureaucrats are ignoring you; it's because governments are very risk adverse. Politicians and high-level execs are afraid of different people hearing different messaging, or classified/outdated info being released accidently. So, the responses have to get approved through a lot of levels of management; the lower levels are focusing more on quality, and the upper levels are just making sure that the messaging is consistent and not leaking anything. It takes a frustratingly long time to get those higher-level approvals unfortunately, but that's just because the senior execs have so many different things on their plate and it all gets triaged (AB Infrastructure currently has 247 active "action requests," which encompass decision points, meeting packages, public correspondence, etc).