What’s the reason for the zero article after a preposition and countable noun in “a change of X” and in “a switch from X to Y”?

To my knowledge, the article, noun and proposition “a change of” does not restrict your grammar choices for government.

An indefinite mass or plural noun does not require an article. If you are using the noun government as an indefinite mass noun (i.e. referring to the essential nature of government or the condition of having government [what you mean by “generic way]) then you choose not to use an article – also called choosing the zero (null) article or zero-marking. Avoiding further specificity by not adding an article forces you to consider the essential nature of the thing the noun names.

The following are all grammatically correct:

• a change in government
• a change in governments
• a change in a government
• a change in the government
• a change in the governments

And so are:

• change in government
• change in governments
• change in a government
• change in the government
• change in the governments
• the change in government
• the change in governments
• the change in a government
• the change in the government
• the change in the governments
• the changes in government
• the changes in governments
• the changes in a government
• the changes in the government
• the changes in the governments

These are all grammatically correct and have different meanings.

• What I want to see all around the world is changes in the governments that are most strict. I want them to become less strict.
• The changes in the governments of Northern Europe in the latter half of the twentieth century were a response to the horrors of World War II.
• You are unlikely to see a change in a government unless the people of that nation are empowered to protest.

I also made a switch from of to in because in works better with all these other variations. But let’s consider that difference as well.

• What we need is a change in government.
• What we need is a change of government.

These two sentences use government as an indefinite mass noun, which means we are mainly concerned with the governance of the country. The sentence with in implies that an internal change of the current government is acceptable, such as a change in foreign policy. The sentence with of implies that the current government needs to be replaced by a new government (through election, coup or revolution) to achieve the change of government we ultimately want.