One reason -- perhaps the main one -- is history. That is, at some point in the past the church or association was more Calvinistic and changed over the years to being less Calvinistic. Even though they changed, they did not change the confession they had (and possibly now just reinterpret it so that it means what they currently believe).
I think there's certainly a lot to that. Truth is, IMO, many, many Baptist churches don't give much thought to their confessions, if they adopt them at all, and they do not expect members to adhere to them — until there's a big controversy.
The New Hampshire may be popular in some limited circles, but it is really Calvinistic in soteriology, though of the Fullerist "duty faith" variety. I cannot see how an Arminian can affirm its soteriology.
(The only local church I know of that affirms the New Hampshire is an independent Baptist church that is TULIP and also affirms the Textus Receptus and is modified KJV-only.)
I am more familiar with Southern Baptist churches, which quite often offer the Baptist Faith and Message as their statement of faith.
The American Baptist Churches in the USA are allergic to statements of faith, preferring to have a statement of identity. The Free Will Baptists affirm a frankly Arminian soteriology.
The BF&M, having gradually departed from the New Hampshire upon which it is based, is quite capable of being accepted by either Calvinists or Arminians. But not semi-Pelagians.
In my half century of being a Baptist, I have never been asked to affirm a confession. I attend a church whose confession I do not really care for, being Augustinian in soteriology and rejecting some of the recent additions to the confession. Somehow we get along.