What about in the case of a password reset request?
Ultimately there has to be some mechanism for a password reset, and there must be some level authentication during this reset.
How about a non-security-sensitive website which has a registration function and the only form of contact is via the registered email address? Users are likely to forget their passwords. The only way to verify a user in order to reset his password is with his email address. If you reset the password on request and then email it, then there is effectively a DoS there, and you are requiring the user to take extra effort (going back in and changing it again). If you email the existing plaintext password to him on request, then there is no DoS issue and minimal hassle for the user - provided that the security requirements make it acceptable for 1) a plaintext password to be emailed (but otherwise what else are you going to do?) and 2) the old password to be continued to be used even after it has been emailed in plaintext.
I'm not sure which of the two options I would implement myself. I'm not even aware of what existing webapps do since I use a password safe and so have never had to go through the process.
I'm just saying that for a non-security-sensitive situation, I have no major objection to the second option being used, and in this case it makes sense for white space to be not permitted in passwords. Since I'm not convinced that there is an entropy advantage in allowing spaces, I don't see why banning whitespace is a problem.