At the moment, changing the profile picture on behalf of a user can't be done by the administrator. Only the account owners can change their very own profile picture. Administrators of managed accounts don't have a direct access to personal content that the user create or update on their profile. For example, an administrator won't be able to change/upload the profile picture posing as the user.
In a situation where you have inactive users but would still like to keep the data but not the profile picture, the admin would require to change the profile picture on behalf of the user. Or in a case where a standard of profile picture must be met, a full control/access to profile picture would be really helpful.
In the managed account, change the email address to any email address that you'll be able to access, verify it and access https://id.atlassian.com using the updated email address. Upload a new profile picture and go back to the managed account page to revert back the email address.