However, when I come to produce engineering drawings from the same model I can select any combination of sides and angles to dimension because these are derived from the model. I would choose whichever best suited the downstream process - in my case, what I needed to make the part in my workshop!
Actually, it can be a bit worse than that. You need to understand and choose appropriately so that you don't lose the design intent, when making choices about which dimensions to carry through to your production process. With the right-triangle example, if you choose to carry the hypotenuse and the two 45 degree corners down to your (let's call them) "shop drawings", and you faithfully produce parts to that drawing, your triangles will _not_ have 1-inch long sides, and you will have failed to produce parts that meet the design intent.
This is a bit of a contrived example (though completely real, and it's terribly easy to land in this situation in a less-contrived drawings as soon as you have anything other than parallel or perpendicular features), but, given this drawing, a) how long is the block, b) what is the angle the sloped section makes with the horizontal, and c) if you, and two other machinists independently choose subsets of those dimensions to carry down to your "shop drawings", how likely is it, do you think, that you will all produce parts that are identical?
(This doesn't even /have/ derived dimensions - all of those are true dimensions, to the precision at which I'm working. And yet, even without derived dimensions it's still confusing as !#@$, because it was dimensioned by a lazy person who didn't think about conveying the design intent. Derived dimensions that are not clearly understood as derived, _or_ not clearly understood as to _how_ they were derived, make hash of understanding the design intent even more quickly. This is part of the reason why it's often important to leave the job of deriving the dimensions to the machinist, or process-design engineer - then they understand _how_ the derived dimensions were arrived at).
Overdimensioning is a curse. I quite like _derived_ dimensions (when they are represented as derived), but overdimensioning, when it's not obvious which are the derived dimensions, ablates the downstream user's ability to understand the design intent. "Shop drawings" that omit design dimensions in favor of "more relevant to the machining process" derived dimensions, make it impossible to determine whether the thing you're making, meets the design specifications. "Instructions", as proposed by William Mays, when they are produced with a knowledge of the design specifications, are wonderful, but they can rarely be used to check compliance with the design spec.
I really don't want to call the hue and cry for "gimme all the dimensions" a product of laziness, but a good designer or draftsman puts considerable effort into choosing the appropriate dimensions to represent, so that the design intent is properly conveyed. Studying those choices, and arriving at an understanding of the design intent, is part of what should be the machinist's job, and should be part of the treasured skill set that sets the machinist apart from the ape.
I would never argue that that job should be made harder by the provision of badly-dimensioned drawings, and lord knows CAD programs produce some awfully lazy "draftspersons" and badly-dimensioned drawings. However, this job or hobby should not be "Oooh - Numbers! Grugg turn dials now!".