If the application or source code is distributed then sometimes removing the license would be a violation. But most open source licenses allow you to make private forks that you keep private. If that is your desire then changing out the license disclaimer to say "Some or all of this code is the property of X, do not distribute under any circumstance" actually makes a lot of sense. If the original license was left in place it would be easy to think that the files in the private fork where publicly distributed. Obviously they don't have permission to change the actual license on the originally public content.

It seems like a very bad idea to remove a copyright notice from a file. Suppose the next developer to see the file doesn't know its origin, then incorporates it into a product that is distributed.