You've mentioned declarative, which is your start. ね can be used as a mild declarative/assertive, but it's weak and softens, which makes its really good for seeking agreement, confirmation AND feminine speech, which seeks to be less assertive than masculine speech.
熱い(です)ね - It's hot, isn't it.
便利(です)ね - It's convenient, isn't it?
学生(です)ね - You're a student, aren't you?
だ is declarative and more assertive than just ending a sentence without it.
猫だ - It's a CAT! (argumentative?)
猫 - It's a cat. (think of a little kid showing a picture they drew)
But sometimes the softening effect is reversed:
猫だね - It's a cat, right? (soften declaration)
猫ね - It's a cat, isn't it? (strong assertion)
よ, in feminine speech doesn't need to take だ because then it becomes too assertive:
猫だよ - It's a cat, y'know! (strong declaration, but not necessarily aggressive)
猫よ - It's a cat, y'know! (softer declaration, but not necessarily non-aggressive either, depending on context)
Sometimes women will double よね for an especially soft declaration:
猫よね - Well, it's a cat, y'know, right?
Men tend to speak more assertively than women, so わ, ぞ, and ぜ require the declarative だ as a matter of course. な, being stronger than ね, is more declarative and needs to follow the rules.
「まあ、ふきのとう。春なあ」sounds weird because dropping the declaration makes it sound like you're talking to yourself where rules might be more lax.