Sometimes it can. Really depends if you have error logs enabled or not. Really helps determine if it’s syntax error or inconsistency. Also, sometimes, blank pages can occur from not doing anything with non-existing data. Such as pulling data from your database and then not doing anything if the data doesn’t exist.
Similar to what you mention. For all PHP controller scripts I have taken to omitting the closing tag, not that it should matter in most cases.
Then in my HTML templates, where the bulk of code is html, with odd bits of php inserted here and there, I obviously need closing tags.
Error reporting is the one to tell you that. That is the point @spaceshiptrooper is making.
Whether you have on-screen error reporting enabled of your local dev environment, or errors recorded to the log on the live server, those white screens should come with some explanation which will help you identify the source of the problem.
One of the reasons (trying to recall) is you avoid problems from having any unnoticed whitespace after the tag, which could have potential to to cause problems with headers or sessions, as the must be no output to the browser before them.