Good news - Single-touch access to the Tempo Settings page is already available. At the top of the screen, touch the third icon from the right. (The icon looks like a quarter note with a number beside it.) From there, you can either tap the large Tap Tempo square on the screen or tap the Enter button.

Since unit multiply is assignable to scene - you can use a single-button (scene) to correct a half/double error in the tempo by pressing the appropriate scene button to double or half the tempo by the appropriate unit multiply setting. This doesn't do exactly what you want - but the tempo recognition is unlikely to ever be intuitive about the desired feel when it's just counting pulses. You may know it's a "2" feel - or a double-time feel with faster (or slower) primary pulses. But the tempo alg. is unlikely to pick up on this sort of thing unless you are able to feed it some form of a hint. In this case, unit multiply may put you in a better ballpark so it guesses correctly more often than not.

@Keven - the OP seemed aware of the shortcut to button-tap tempo. The request was to make this even more direct and remove the need to push shift. So a touchscreen gesture is likely not going to be OK - although this does enable a "no look" one-handed solution if your muscle memory on the touch screen is good.

Insert my usual request to assign a dedicated knob for increasing/decreasing tempo. Tempo as a destination for using an assignable knob (with or without superknob link) would work. Or some other knob solution (not an offset - direct control).

Keven,
I use the shift function to enter tempo section, because it's easier than the button on touch screen: too small and the screen not reactive enough, I miss it each time during the show!
The solution is a single tap tempo button.

Not now - for but for the next generation of Montage - or GenOS - or whatever is coming down the pike - I'd like to see the tempo knob come back and can dual-purpose with a "push" style knob where you can tap the knob for tap-to-tempo. This would put all tempo related gestures into one place - a dedicated tempo knob (for increase/decrease) with a push function for tempo-tap. No need for [SHIFT].

In terms of what could be done today without changing hardware -- we'll see if anything happens this go around.

I guess you could always find a device which generates a MIDI clock and does a tap-to-tempo in an easier way than Montage (no touchscreen, no shift) and slave Montage to this device.