Obviously anecdotes are everywhere, but at my work I never had any issue saying "we will need 2 weeks for research on how to use this technology", if you say you need 2 weeks to assess something then you need 2 weeks. What, my producer is going to tell me that I need less time? Based on what?

I think your issue is that you're doing open ended research - if you don't specify upfront how much time you need to investigate something then no wonder you're being asked for updates after 2 days.