Anything can be realised with off-the-shelf technology plus time. Your posited solution further down the page would also have involved work in setting up the pool configuration and switching, so let's not pretend that it comes at zero cost.
Efficiency is a major problem in government. Government should have a low financial impact on society where possible. A government entering a market with an already solved problem is wasteful at best. If they'd contributed time to Nginx or mod_proxy then they would have a net positive social effect.
But they didn't. They built an inferior product at great cost to the taxpayer.
Is this some sort of Markov-chained free-market/El-Reg-at-its-most-prolix/libertarian experiment in satire? Well played!
Various governments are already throwing money at Open Document Foundation (France, Germany come to mind) to support LibreOffice so why shouldn't we throw a few quid at nginx/apache?
Or should we go and write our own office suite?