Well, I have been thinking about it recently.
DS1 has had tonsillitis a few times this winter (I used to get it A Lot).
He's just getting over an ear infection (again, I used to get them A Lot).
He has very mild eczema (as do I - actually, mine worse than his and flares much more often).
DS2, on the other hand, gets the occasional sniffle and has vomited once in his two years.
DS1 is 3.10 and was bf for 17m, DS2 was 2 last month and still bf. Neither have ever had any formula.
So both fall into the category of bf for longer than your average bear.
So I guess for some people, DS1 would fall into the "sickly bf child" category - or rather, "sicklier than my ff child" category. He's farm-child healthy the rest of the time, but seems prone to these ENT things.
And this is what I mean by not thinking it through properly - how would DS1 get tonsillitis or ear infections less frequently if I'd ff him? That's rhetorical, btw