If businesses didn't make promises before they knew if they could keep them, the deadlines wouldn't be such a problem.
If an employee agrees to a deadline, it's fine. If an employee is just told they have to complete a task within a deadline that they're weren't included in estimating, that's not the employee at fault.
An interesting point on developers who refuse to estimate, is how often they are then asked "Why ?".
I'm definitely someone who has either refused to give, or given massively exaggerated estimates in the past, for various reasons, the main being "I don't know".
Think about this for a moment - why wouldn't an (experienced) engineer know how long something will take ?
The most likely answer (and in retrospect the only reason I ever did this) was that the project was far too large / complicated to visualise, and needed to be broken down.
By asking an engineer to break the task down into smaller tasks, until they can 'ballpark' estimate each part, is the best way to solve this problem. Maybe more design or investigation will be required to manage the breakdown.
Instead of writing off 'problem' engineers, try to work with them and find the common ground.
If an employee agrees to a deadline, it's fine. If an employee is just told they have to complete a task within a deadline that they're weren't included in estimating, that's not the employee at fault.