Your comments

This is a bug. It turns out that if you open an input panel, then any output panel or "quick panel" will be immediately closed after the onDone callback is executed.

Here's an example command that reproduces the behaviour. When you type something and hit enter, the quick panel will be displayed briefly, and will then disappear.

class TestCommand(sublime_plugin.TextCommand):

  def run(self, edit):

    self.view.window().show_input_panel("Type stuff:", "",

      lambda s: self.on_done(s), None, None)

  def on_done(self, s):

    self.view.window().show_quick_panel(["one", "two", "three"], None)

The "Go to anything" (cmd+P) command currently does what you're asking for.