Ugh. I don't actually miss the onscreen start button (although I can imagine the discoverability hit to casual computer users). I miss the actual start menu, which was vastly more useful than the gimmicky thing they replaced it with.
What about it was more useful? I didn't change any of my habits after upgrading to Win8. It was only a cosmetic change as far as I can tell. I still just hit the start key and start typing to launch things, search for apps and files, or run commands. Meanwhile the new start menu also lets me search any app that registers itself as a search provider (i.e. search through my Kindle books, my Netflix account, etc), which is handy.
Universal search: I didn't have to choose "Files" "Apps" "Settings", etc. It just floated whatever answered the query.
Outlook Integration: I could search emails, files in email attachments, and files on disk with one query in 7. As far as I can tell, Outlook 2013 wants nothing to do with the TIFKAM search at all.
Not full screen: I would routinely transcribe something onscreen or drag something out of the search results into a window.
If there was any upside to the weird new menu at all, I could deal with these changes, but as far as I can tell it's pure regression. Windows 8 has lots of tiny technical advances, but the shell changes are just a disaster.
For me the worst thing is that I get completely thrown out of context. Usually I've got 3 apps open, I quickly need to bring up another window to do something (say, calculator to do some simple numbers) and now wham! my whole context is gone, my brain is jolted out of the 'flow' that I was in. It's a mental thing so it is hard to explain, but I just find it jarring, unpleasant, and kind of hostile, like someone coming into my office every 10 minutes and shouting in my ear or something.
But if you want a practical consideration, the start 'menu' now obliterates whatever I was looking at. So say you were following instructions in a web page (open start menu, type 'control panel', click in menu ...) - well you can't, because the web page you were looking at is not visible now, all you can see is a bunch of stupid tiles trying to distract you from what you actually wanted to do.
I miss jump lists on pinned start menu items. I never liked pinning things to the taskbar because when you run those apps, the launcher becomes the taskbar item and you lose the launcher. So I always pinned things to the start menu. Now I can't do that and have the jump list.
I also miss Microsoft being the non-walled-garden OS company. There's no way I'm granting them a monopoly on what can and cannot be installed on my general purpose machines. If there's one thing I hope they change - it's this. Let me install Metro apps from whatever source I want.
1. Start menu 2. Tile size
(source: http://www.pcpro.co.uk/news/380713/windows-blue-8-1-release-...)