The structure of government is one thing. The written rules and laws it is to follow is another thing. And the people selected to fill that structure and work within those rules is a third thing. In the minds of most people, those three things tend to blur into a single entity called "government". By calling for prayers of thankfulness for the structure of our government, and for our set of laws, one is also calling for prayers of thanksgiving for incumbent office holders at a time when the incumbents are being challenged in contested elections. Such prayers would be heard by many people as an endorsement for incumbent officeholders.
I'm not sure what distincting you are trying to make between the first and second points. Of the second you said the laws it (meaning government?) is to follow....Wouldn't that be the structure that arranges how the government works? Perhaps you mean the enactments of the government. As to the people that fill the structure some are elected others but many perhaps most are career civil servants. They are good because the do the work of governing, not because of policies they enact. (Caveat: if what they were doing were manifestly criminal, violated the laws they have a duty to uphold, then they would be poor servants worthy of rejection through election or termination of employment on behalf of the public.) How can affirmation of the work of civil servants partisan?
"Structure" refers to such things as a bicameral legislature with separate executive and judicial branches. Laws refer to those things that the legislature passes that the executive executes. If a city with a home rule charter decides to govern itself with a pseudo parliamentary structure, with an elected council that appoints one of it's members to be the chairman/executive, that's a
structure. If a city has an elected council and hires a professional city manager to handle the executive duties, that's another structure. If the city has an ordinance requiring people to keep their sidewalks clear of snow and ice, that's a
law. Jurisdictions can have different government structures, and yet have similar laws. Likewise, identical structures could result in very different laws.
A jurisdiction could pass a law that all persons must have a properly approved permit in order to build an addition to their home. The bureaucrats responsible for issuing those permits might be good and diligent public servants, or they might be incompetent fools. They might do their work as they are supposed to, or they might require the illegal payment of bribes before they do what they should. A jurisdiction might pass laws about restaurant sanitation, but the bureaucrats who do the inspections might be incompetent, corrupt, or both.
There are also laws such as constitutions or charters that specifically limit what authority a jurisdiction has. The US Constitution limits some functions to the Federal government, and reserves other functions to the states or the people themselves. In modern times, most of those limits are blatantly ignored by the use of the weakest, flimsiest excuses. A recent example is Federal taxes on people who don't buy healthcare insurance. It is true that most constitutions and charters both define structures of government as well as setting limits on them, those are two separate things.
And far too often, when the bureaucrats responsible for carrying out the provisions of the laws are incompetent, corrupt, or both, it is because their jobs were obtained as a result of political patronage.
