One thing's for sure, no modern well-known browser is going to care. Indeed in HTML, as opposed to XHTML, the </html> tag is superfluous too.
However, in your first sentence you ask for microscopic reasons and I have one. Some editors (I think notepad used to be one, I haven't checked lately) will automatically add a CR/LF to the last line of a file on save if the line is not empty, probably to fix problems such as the ones DevelopersDevelopersDevelopers describes. This used to be a real irritation when editing DOS batch files as an extra line could adversely affect the way the script terminated.
As a result, if you create your HTML in one editor which doesn't do this, and you don't manually add the final CR/LF, then later someone opens the file in a editor which does, doesn't change anything and saves, you get an erroneous difference that can show up in when searching for real changes or in version control logs.
In your second sentence, you ask for significant reasons. This is not, IMO, a significant reason, and I certainly would bother about such an edge case.