wow ok, your team is great then! I was part of teams that didn't used but we ended up regretting.
I usually saw linters solving a lot of (very small) problems in large teams and projects, like (forces a coding standard, find small bugs like forgetting to type a var or forgetting a switch default, fewer git merges/conflicts) which leads to a better codebase in general (if you enforce the rules at commit/build).
As a sidenote linters are builtin in most IDEs so maybe you use them already, but only at a basic level.
We use eslint (for the older projects, a combination of jshint and jscs). The plugin I use for vim (ale) works with pretty much any kind of linter I've encountered.
This isn't the sort of static analysis I'd expect from and IDE though, this is what I'd expect from any kind of programmers editor (vscode, sublime, etc). What I meant by static analysis is the ability to goto definition, display documentation, refactor, etc. This is the sort of stuff which doesn't work consistently enough with our codebase to even bother trying.
"The beautiful thing about vim-as-a-concept is that it's available in some form or fashion in nearly every IDE and text editor."
Personally I'm yet to find any implementations that replicates vim entirely. In every single one I tried I stumbled at something that just didn't work (often f/F/t/T, or ci( are missing, but even in the best "vim-mode" I've been working with so far there was something missing).
"What I meant by static analysis is the ability to goto definition, display documentation, refactor, etc."
You can have all that in vim. Look at YouCompleteMe.
PS. I'm not trying to say vim is for everyone - it has a very steep learning curve, so unless you don't have time to spend learning it, stick to IDE. But for those who did learn how to use vim any IDE gets obsolete.
PS2. I'm working with pretty much bare vim - at the minimal I use only YouCompleteMe, language-specific omnicomplete if needed, vim-gitgutter, syntastic, vim-autotag, and vim-polyglot. And still the ability to move through the code fast exceeds what I'm able to do in other IDE. I do have some shell command trickery set up in my .vimrc though (nnoremap to various !find [...] and !grep [...] shell commands)
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