Well, programmers should use whatever they feel comfortable using. Sure Vim and Emacs have a much steeper learning curve and they are also much more productive and powerful once you master them, but it dosn't work for everyone.
For starters, if you have your hands on your keyboard, moving them to reach the mouse takes time, so if you can do everyting without moving your hands, this is something that improves your workflow.
Secondly, even moving your hands on the keyboard to reach for the arrow keys makes you loose time, so if you can do the same without moving them from the main row...
On third place, with Vim, once you master navigation you moove pretty fast. You can move to the end/beginning of the next previous word, etc, and specify the number of times you want to do that just by prepending a number before the action. You can use regular expressions to search and replace (yes, I know, you can do that with other editors as well).
And many more advanced, powerful features and shortcuts that you learn over time.
You can just ssh to any linux/unix and edit a file really quickly. On some boxes it's the only editor available. This one alone is a really good reason to learn at least the basics of Vim.
Then, it's a personal choice. I force me to use it and learn and improve, but because I want to master it, you might not have the same goals as me. And of course you can leverage what you already know about Vim without giving up the benefits of other tools. For instance, you can prefer to use an IDE instead of just a text editor for some programming languages, so you can just use Eclipse, IDEA... along with their Vim plugins.
Of course you can configure Sublime Text to use Vim keybindings as well, so you can have best of both worlds.
Overall, I guess it depends if you like commandline. I love commandline, so the ability to have something like tmux over ssh + vim is really powerful once you know how to use it.
In the end, it's a matter of personal preference.