Can a bank under any circumstances charge the borrower for an appraisal at time of application? Isn't the credit report fee the only fee that can be charged at application? What is the earliest point we could charge the borrower for an appraisal fee?

Once they indicate intent that they wish to move forward with the application they have submitted to your bank. That could be at the time of application, it might be two weeks later.

Also, if the loan isn't subject to RESPA (land only, non-owner occupied rental property, etc.), then you don't have the 'intent to proceed' technicality to worry about.