I had a mentor who was very much of the view that "funding begets funding" (his words). Perhaps not so relevant for PhD level funding, but in biomedical sciences I've heard research councils freely admit that if a candidate is funded by them for, say, a junior fellowship, they are considerably more likely to be successful if applying for an intermediate or senior one subsequently.
It may vary from field to field. You rightly point out other features that may take priority. But it probably does come into play if all the other factors are fairly equal between two candidates.
Agreed, and I can certainly imagine that being more the case in the biomedical field as you cited, where results are absolute and speak for themselves and "poorly conceived proposals" are more likely to result in "useless results" that add no value to the field. That being said I always leave room for the rare unfunded genius :P
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