Having a specific kinase inhibitor can work well in very defined one hit cancers, as in the case of Gleevec inhibition of the abl kinase activation via the famous Philadelphia chromosome translocation. However, having a single kinase more specifically targeted means it is easier to generate resistance by activation of other growth pathways.
I am not sure that y'all are in the disagreement that you think you are. More a disagreement on degree than in kind - ultimately biotechhedge is asserting that in the following 2 scenarios the second is better:
a) One drug which targets, say, 10 distinct targets
b) Ten drugs which each, independently, target 1 of the 10 things targetted by the broad spectrum drug. Then you determine for each individual cancer which 1, 2 or 3 (4?, ...) of the 10 targets it is susceptible to and use only those drugs.
Hard to argue with the assertion that #b is almost certainly a better treatment modality. The only real uncertainty comes about when, for instance, you only have 1 (or 2 or 3...) of the 10 drugs you need to make #b true. How many do you need to have to make a spectrum of individual drugs better than a single multitargetted drug?