I’d say you can use have instead of have got in any context but not vice versa.
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The verb have has more meanings than have got and, in addition, I think it would be best to avoid using have got in a formal context.
In informal, spoken American English, people often drop the 've in “I’ve got” and what you end up hearing is something like “I got three brothers and one sister.” or “I got a headache.” In both cases, the meaning is “I have…” (present tense). 8)
P.S. Now I don’t only know, what would happen with the idiom if I changed Presents Simple to the Past Simple - ‘I had a lot of time for…’. But I suppose, nothing awful?..