It depends on the state as each state has different ballot access requirements for down ballot candidates. Say you want to run as a Green or PSL candiate for state office. Does the state recognize the party and thus put your name on the ballot without having to resort to costly signature drives for both party recognition and putting yourself in as a write-in?

Many of them have requirements of X% of the vote of Y office for their major candidate in the last election. Major candidate being the Presidential candidate. You'll have the whole state vote for president rather than a single local district office. Much easier to get say 20k votes from the whole state rather than one district.

I.E. Michigan

Maintaining party status

In order to maintain qualified status, a party's principal candidate (i.e., the party's candidate who receives the greatest number of votes of all candidates fielded by the party in a particular election) must win at least 1 percent of the total number of votes cast for the successful candidate for secretary of state in the most recent election for that office. For example, in 2010, 1,608,270 votes were cast for the successful candidate for secretary of state, meaning that a party's principal candidate had to win at least 16,083 votes for the party to retain qualified status. A party that fails to meet this requirement must petition again for state recognition.

So for example, if you want future Green party down ballot candidates to be able to have an easier time getting on the ballot, Jill Stein (Presidential Candidate) needed to 16,083 votes for the Green Party to keep their status in Michigan ballot elections. Otherwise they would be subject to grueling and expensive (which are getting worse as 3rd parties become more of a real threat) signature drives to regain their status with the state.

Yes there are advocacy for issues, and promoting the party that comes along with it.

The after effects of Nader yielded a few states getting over 5% percentage for the Greens as Governor candidates.