Think about why it might be that they don't respond well to this request. Don't just assume that they're lazy or avoiding effort.
Developers who avoid producing evidence are usually
- Worried about how it might be used and/or
- Concerned about the validity of the data
This is why points-based estimation and shirt-sizing has taken off in recent years. It takes into account the very uncertain nature of the process of estimation and allows for "magic" (aka, averaging out of the uncertainties) to take control of scheduling.
And, while it may not seem logical, it does mostly work - at least as well as an hour- or day-based system. It is also very difficult to batter a team or individual around the head with what they've achieved in a month if it's done in an arbitrary way.
Scrum also allows developers control over the velocity, which means that they are making a promise to achieve whatever you choose from A, B and C or A, Y and Z. When they've made that promise, developers do not like to fail; but if you make that promise for them, they won't care. It's your fault if it's wrong.
I understand that you're saying you wouldn't use the reestimations in that way, but how sure are the individuals on your team of that?