I agree 100%. But saying that using trim will make the site not work isn't true - as long as you trim it every time.
Not to mention, that a simple phrase is way more secure than just "random" characters. You can make a much more secure password using only a-z than using special chars - what matters is the length.
You said
"I click "Register" and the form goes through successfully. Now, in the backend you've just trimmed that trailing <SPACE> without my knowing. The next time I go to login my trailing space is no longer valid and I will have no idea why."
That is not true, as long as they trim it each time. That was all.