To me thinking in keys can be problematic as it can make you think of a melodies as certain white notes rather than a pattern that can be transposed to all keys
Well, "thinking in keys" should be exactly like that.
Starting from a key that has lots of alterations (for instance, Ab) doesn't offer real benefits, and since beginners need to grasp lots of concepts in their first lessons, there's really no reason to make things even more complex than they are.
Most methods use those two tonalities (often along with G major) for various reasons, but mostly:
- beginners are usually children, with small fingers and relatively limited control on their "finger coordination" (a white key is much easier to press than a black one);
- the concepts of tone/half tone are not immediate, especially by looking at a keyboard: the "spaces" are not even in different tonalities, children usually have a simpler perception of distance, and to them (but not only) moving between a white and a black key means doing a bigger distance than between two white keys;
- both scales, especially in the first 5 degrees, offer easy visual response of intervals, with the benefit of allowing introduction of alteration for the Bb in F and simple transposition (they usually go with something like "it sounds strange" when pressing the B-flat key for the fourth degree);
Actually, many methods use the "Movable Do" system, which is very useful as it introduces the concept of scale degrees and the relations between them, more importantly if done along with singing.
Using numbers might seem a better approach, but it implies that some level of good abstraction already exists (which can be difficult for some tonalities just by looking at the keys) and, considering that numbers are normally used for fingering, it may create further confusion (that's why scale degrees use roman numbers).
So, using tonalities with few (or no) alterations is usually better for lots of aspects, but it should also be done with awareness. You should not "focus" on the tonality itself, but on its concept and the relations between its notes.
In this way you then can begin to think in any tonality from different aspects, with a higher level of abstraction that almost ignores the actual keys you're pressing.