First, I don't know vi. Well, I am aware that something like this exists, because I see "{not in vi}" everywhere in VIM docs. So maybe you should familiarize yourself with VIM before talking about it - for example I noticed that you wrote that "[in modern editors] there is no need to wonder in what mode you are" as if it was a problem in VIM. It's true for vi, but VIM has a mode indicator on a status bar since times immemorial.

Second, in VIM there are three modes, that's true, but not the ones you enumerate. There is: insert mode, normal mode and visual mode. All modern editors have at least the last one: the editor (all of them) behaves differently when you have some text selected.

Third, in VIM you can freely delete and navigate (with arrows!) in insert mode. No problem at all. Even things like ctrl+left for to skip a word backwards work.

Fourth, sheer amount of commands and functions makes the cheatsheets you mention valuable, they are not needed because the functions are so weird, they are needed because there is so many of them. I saw cheatsheets for Word and Photoshop too. You could argue that paint is better than photoshop because you don't need a cheatsheet to use it, but I doubt you'd want to do that. It's the same for editors: you don't need a cheatsheet for notepad...

Fifth, VIM evolved to the point that it is effectively a platform for building text processing apps, similar to Emacs. There's VIMScript and Python, Ruby and Lua support. With this there is practically no limit to what you can make VIM do for you.

To summarize: you seem to mistake VIM for vi; please take a closer look at modern VIM and then come back with a critique that makes sense in 2013.