It should be obvious that government agencies lack the incentive (generally profit and the competitiveness necessary to maintain it) to meaningfully address and/or eliminate problems. Nor do they experience any significant downside to failure. They aren't legally accountable to shareholders and it certainly isn't their life savings that they stand to lose. Worse-case scenario, they're reassigned.
Government agencies aren't expected to innovate, they're legally required to carry out the will of Congress and do absolutely nothing else but the will of Congress.
Most of the "failures" you see are the result of a dysfunctional political system. For example, the Post Office was looking to branch out into services like bill payments, identity verification, banking, etc but Congress forbid them from doing it. Not to mention the crazy requirements Congress set for pre-funding their retirees. No private company has to do that - most of them are pushing their funding obligations off to the future. Underfunding retirement isn't a good idea by any means, but the playing field is most definitely not level here, both in terms of responsibilities or ability to pivot.
It's wildly unfair to blast government agencies for not innovating. They don't have a CEO or a board, they have Congress calling the shots. Of course they aren't agile. And even worse, half of Congress thinks the entire concept of government services is illegitimate and is actively engaged in sabotaging and defunding those services. There's not really a parallel in the private world where a CEO is destroying a company because he thinks it shouldn't exist.
