Whether this a noun phrase or not, depends on your grammar. However, the more important point is: Can we use "For someone to do something" as the Complement of a verb (or indeed as the Subject of a clause)?
The answer is like this:
We can use to-infinitivals without the word for:
- To err is human.
- The best thing would be to give the elephant a bun.
- I arranged to leave.
In the sentences above there is no for introducing the infinitival clause. However, notice that these clauses have no Subject. Often, if we want to use a Subject with an infinitival clause, we need to start the clause with the word for:
- For people to err is human.
- The best thing would be for Bob to give the elephant a bun.
- I arranged for the ship to leave.
The Original Poster's sentence is grammatically correct:
The best approach to address this issue is for the government to introduce green taxes.
This verb uses an infinitival clause as a Complement of the verb BE. It is a grammatically formulated sentence. The reason that for is required here is that the infinitival clause has a Subject, the government. If we don't use it the sentence is ungrammatical:
- *The best approach to address this issue is the government to introduce green taxes. (wrong).