It does, but I want to do it with an Alfred-like switcher.
The problem with *-tab is that each application has no fixed place in that space. So on every invocation I have to look, find, switch.
Contrast with bringing up Mail using Alfred. The behaviour is always the same, and therefore muscle-memory-learnable: Cmd+space, ma, return. Messages: Cmd+space, me, return. Near-instant for me because I've done it literally thousands of times.