No you don't, HTML has massive variation between devices and what software is used to display it. Try setting your screen resolution to 640x480 and opening a webpage or, even worse, modifying DPI. PDFs on the other hand specify exactly where to place each glyph (admittedly there is still variation between software but it's much more consistent).
You sure do - the variation between devices is the manifestation of the ability to control layout depending on the recipient's display's resolution and size.
If anything, a PDF designed for A4/letter is going to be cumbersome to read on a (probably rather small) 640x480 display.
The sad state of PDF rendering on (most) e-book readers should be evidence enough.
More control over how it looks at the users' end with HTML than I do with Latex? Yeah, I don't think so. Why would everyone be using JS if you could do whatever you needed in HTML?