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I'm not a teacher
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In this particular example it seems it's just a matter of collocation.
Interestingly enough, you use the formula with "have a something" when the pleasure of the subject and no particular purpose are involved (that's not the only way you use the structure though) e.g.
1. I had a walk/ stroll/ swim. :tick:
2. I had a walk to my friend's place. :cross:
- It might be pleasurable for the subject (you), but it serves a purpose - you want to reach your friend's place, it has a destination point
3. Every weekend we had a walk around the pond. :tick:
- You can say 'where' but not for what purpose
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P.S. You can find more information on this and similar structures in The Semantics of Grammar by Anna Wierzbicka. The chapter's titled Why you can have a drink when you can't *have an eat.