I agree on all fronts. I am just rather surprised that Bond films have strayed away from continuing stories within each era. You can start all over again when you have a new actor, but it seems perfectly reasonable to have interconnected elements within the same series. Maybe that is just a modern notion though… one which Bond is only recently trying to imitate. For me at least, such a thing would make Bond films much more interesting and worth watching. Without a greater story arc (within a series), it feels like you have to constantly define who this Bond is and why what he is doing this time around is meaningful or even difficult for him. Without that struggle for growth, all you have is a veneer of explosions, guns, women, cars, one dimensional evil geniuses and exotic locales. In my opinion, the writers should try less to modernize the items within the formula; these will take care of themselves. Rather I think it would be much more interesting to explore the facets of Bond himself: his motivations, history, pains and fears.
Bourne is quite different from Bond in many respects; some of which make it unfair to compare the two franchises. Bourne is less of a pop culture icon and has a more limited story line, not to mention a much smaller screen history as you pointed out. Even so, the original three Ludlum Bourne novels have virtually no similarity to the films other than the basic premise. The movie writers and directors adapted the Bourne story in an extremely compelling and well-executed story for a modern audience. Bond does this with every new iteration, but seems only recently has the Bond franchise incorporated the story arc element. At least from what I have read and seen. - Again, I am no Bond fan and have only seen the last three, minus Spectre.
I don’t know that Bond will ever drop the formula elements. It is what defines Bond at this point and maybe it is wrong to think that they should. I wouldn’t want some know-nothing coming into my franchise and changing the very fabric of it (Star Trek… JJ Abrams). However, a greater focus on the story telling aspect doesn’t have to mean the classic features are dropped. It is just one more way to modernize the franchise.
PS - Bourne Legacy was terrible. I don’t want to see another Bourne movie without Matt Damon as the main star and Paul Greengrass directing. Just not worth it.