In my experience, PM's or whoever usually want estimates on the spot. They want estimates fast, but then they treat them as though they were well researched. If you tell them "there's a 75% probability we can get it done in 2 months" they hear "we can get it done in 2 months".

There's also a tendency to leave out important information. I recently worked on a project where 1) more than half of the features were not in the requirements because the product manager assumed we could re-use existing functionality from a completely separate application (we couldn't); 2) half of the requirements from the new work were left out of requirements because they didn't bother to specify them; 3) a critical requirement regarding how data was to be aggregated in search results (which is the primary feature) was not included because the architect didn't bother to tell anybody about it except for a passing "hey, what if we did this instead" before going on vacation. This caused 2 weeks of re-work after we were done, that would have taken 2 days if we did it from the start.

Our engineering team reviews all requirements as a team before giving estimates and this STILL happened, because we couldn't know what was missing. Good estimates begin with good requirements, and usually the people responsible for those do not end up being accountable, it ALWAYS falls on engineering.