The link you have shared is not working.
There isn't a black and white way of structuring an organization within the public sector. It is not entirely true that all public sector institutions would focus on 'layering' individuals as you have suggested.
Competition, on the other hand, is something that isn't inherently incentivized in the public sector. I've only had a chance to talk to a couple of individuals in the public sector, here in Canada and it seems like and this is just my interpretation that there is a general culture of maintaining the status quo. Whatever the status quo may be. Here, in Canada, the government (as an institution and not political parties) also does a relatively decent job of maintaining the civic infrastructure and for the enablement of smart and effective policies. Political corruption within the ranks of the parties is not in scope when it comes to this discussion. That's a wider debate about Social Democracies, with the consolidation of authority and how it can and does lead to political corruption.
In due course of time, government/civics/public sector is an area that is ripe for disruption. I guess the key question is how to enable 'government as a platform'. In a future state, say 20 to 30 years out, most of the functions could be automated by virtue of making use of a combination of sorts of narrow AI that would have been trained to perform many intended functions (so the sum total of). But that does not stop us from thinking how the public sector (in general) can be made better and better efficiencies can be had by making use of more technology and more design-thinking.
When it comes to enabling change. But it is always, if not exclusively better if you have all intended stakeholders on the same page. Translated, that means that you have to embrace the system and ask the system how it can be changed. Richard Tafel has a great video on the topic of system change. Feel free to watch it here if you'd like: https://goo.gl/X3ro7i
(Richard Tafel: 5 Steps for Systems Change)
Hope this helps.