The best IVR is the one that - doesn't ask any questions (i.e. recognises you by calling nr, and guesses why you are calling)

Agreed, from the perspective of a user, not a systems integrator. The most "friendly" systems I've ever had to deal with were the ones that used the calling number to discern information about who I was and only ask for other information to fill in gaps as necessary.

For example, I recently called Apple to check on the status of a repair. Their system determined that the number from which I was calling also appeared on an open work order, and told me the repair status. Simple and painless, and I didn't need to do any acrobatics like keying in my serial number or the work order number.