When eating a food that requires two brachos (Crispix, some salads etc.) I was told that the correct procedure is to make one bracha on part, eat it and then make another bracha on the next part. Why can't I just make two (or more) brachos and then eat everything?
If you make both brachot before eating, you are introducing an interruption between the first bracha and the eating to which it applies. We make brachot as close as possible to the act that calls for the bracha.
This answer assumes that you are eating two (different) types of food as separate entities. If the food is really one combined item, then you would say only one bracha based on the rules of precedence. See @DoubleAA's explanation in the comments on the question.)
I disagree with Monica Cellio's answer because I think that a hefseik should be permitted in cases where there is no hesech hadaat. For example, the shehechiyanu blessing in Yontif Kiddush is recited after the borei p'ri hagafen but before the wine is drunk. So too here, we should be able to say e.g. regarding Crispix cereal that reciting two blessings one after the other is part of the nusach habrachot for that food and there is no hesech hadaat like kiddush on yontif.
(This hefseik is not unrelated to what you are doing. See Identitytheft-Dave's comment on the initial question.)