The irony is that at least some of the time, a "safe" estimate will actually make the project take longer. Work naturally expands to fill a deadline, and not having a deadline but instead frequent progress checkins with an expectation of foward progress can result in more getting done, because it changes the conversation from "how at risk is the deadline" to "how much happened in the last week and what are the next steps", forcing progress to happen continuously rather than one big bang at the end.
I also often hesitate to give estimates / establish deadlines because it tends to create an unhealthy confrontational atmoshepere, where developers are incentivized to not incorporate feedback or make any changes even if they are the right thing to do, because it would put the deadline at risk (but if they incorprate allowances for these things during estimation it's considered sandbagging).