LEGO has many great Creative Building Boxes, especially the LEGO 10697: XXXL Box
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Why hasn't LEGO come out with a Creative Building Box that consists of Technic parts?
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Sign up to join this communityOne answer is that TLG actually has done something similar in the past. They used to produce universal sets that were roughly equivalent to the Creative Box that you're referencing. Here's an example:
These sets all included lots of basic Technic parts and instructions for 3+ models to get you started building.
This is getting into the realm of speculation, but TLG stopped producing the universal sets right before Mindstorms launched, so I would guess that they felt that Mindstorms filled the free creative building niche and didn't want multiple subthemes in that space. The primary Mindstorms sets include a wide variety of multipurpose parts, instructions for multiple models, and encourage free building and exploration rather than just building a single main model. So, a second answer could be that Mindstorms is the Technic equivalent of the current "Bricks and Pieces" line.
I do think that it would be nice to have sets exactly like what you are describing. I grew up with a few of the universal sets, and they were great. If you're looking to get something like this, it's worth noting that there have been some sets like this recently in the Education line, such as Simple Machines (9689), but those tend to be overpriced in my opinion. You're better off just picking up the parts the you want from Bricklink.
Just to mention there is a book from Klutz "LEGO Crazy Action Contraptions Craft Kit" that might fill in the gap at the lower and smaller side