The level of indentation is plainly visible, but it looks the same (unless you're using an editor that specially marks tabs somehow) whether you're using spaces or tabs. Therefore, the tab characters are effectively invisible.
As for your comment about "wrestling with levels of brackets", what? Do you use Notepad to write code? As someone who likes Python a lot, but is also familiar and comfortable with several other languages, that is utter nonsense. Indenting is fairly straightforward in Python, but outdenting is insane! Let's see, I've got the try block and the for block and the if and the if, and now I need to outdent to match up with...one of those. Which is positioned...somewhere. With braces, it's easy to count the braces, or (in most editors), simply put your cursor on the brace and have the editor automatically show you where the block starts. Furthermore, re-indenting with braces is easy, because the editor has braces to guide it. (Unless, again, you're using notepad or something else unsuitable for the task of programming.) With Python, you have to manually inspect the locations of the previous blocks, and god help you if you outdent improperly, because nothing will offer you any hint that you've done so, except the misbehavior of your code at run-time.
(Let's not even get into what happens in Python if you indent by four, and then by three, and then outdent by eight, or some other doesn't-quite-add-up combination. Python is a great language, but its indentation stuff is its biggest flaw, by far.)