I've really noticed this too and ended up taking your same strategy, especially with programming questions.
For example if I ask for some code and the LLM initially makes an incorrect assumption, I notice the result tends to be better if I go back and provide that info in my initial question, vs. clarifying in a follow-up and asking for the change. The latter tends to still contain some code/ideas from the first response that aren't necessarily needed.
Humans do the same thing. We get stuck on ideas we've already had.[1]
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[1] e.g. Rational Choice in an Uncertain World (1988) explains: "Norman R. F. Maier noted that when a group faces a problem, the natural tendency of its members is to propose possible solutions as they begin to discuss the problem. Consequently, the group interaction focuses on the merits and problems of the proposed solutions, people become emotionally attached to the ones they have suggested, and superior solutions are not suggested. Maier enacted an edict to enhance group problem solving: 'Do not propose solutions until the problem has been discussed as thoroughly as possible without suggesting any.'"