SP, there most certainly is evidence that exclusive breastfeeding to 6 months protects babies' health.
Here is the link.
This is the Millennium Cohort study ie it's from the UK, and they studied just under 16 000 babies for the first 8 months after birth.
They found that "an estimated 53% of diarrhea hospitalizations could have been prevented each month by exclusive breastfeeding and 31% by partial breastfeeding. Similarly, 27% of lower respiratory tract infection hospitalizations could have been prevented each month by exclusive breastfeeding and 25% by partial breastfeeding."
In other words, exclusive breastfeeding has a profound protective effect against serious infection even in a country with clean water and plenty of good food.
In this population, 1.2% were exclusively bf to 6 months. These babies were born in 2000-2002, just around the time of the WHO expert consultation on exclusive bf to 6 months, so probably the figure is higher now.