I gotta tell you that unless you're working with absolute bozos, nobody is looking at estimates and saying "oh duh, I am betting the farm this will complete on that date."
Benefits of estimation that are more important that the date itself:
Enabling trade-off analysis: If you tell me the thing will be done in two months, I bucket the thing in my head as something that takes "a few months" as opposed to "weeks" or "years." Often that is enough to drive a build/pass decision on the feature.
Dependency visualization: If I don't ask you to estimate, you might just start coding. Estimation may force you to think about critical paths and dependencies, then we can plan for them to improve your chances of success.
Troubleshooting: why did we miss an estimate? A task was harder than we thought, that's ok. We missed a dependency, ok that's a prompt to think about those better next time. Developer keeps getting distracted, maybe we need to change something on the team. Estimation is just "calling a shot" which then enables us to (maybe) learn from missing it.
All those things are valuable even if the actual estimated date is missed, even by a lot.