Thank you Krileon,
Then let it be done properly.
First the default value should be set by trigger as you propose for new users
For existing users, if this is new field, the default value should be set for all.
It should be possible to edit the default value after field was created:
administrator should be able to select if the old default value will be changed to new one for all existing users or not.
As temporary solution I managed to handle this issue with custom JavaScript but this is not clean nor nice.
Thank you!