From woodworking you would know that large cross grain glue-ups are a bad idea. A couple of inches on a mortise joint in furniture is fine because the glue will flex enough to allow for that. But the joins in a timber frame might be mortises with 8" or more of cross grain. Now a big mortise joint, with a peg or two holding things secure, allows for some drying and seasonal movement. Without your stress of a cross grain glue-up.
Only place I can see a use is laminated beams, which isn't really traditional timber framing. But it's commonly used in modern wooden building construction, even on quite large multi-story buildings.
Technically there is no reason you couldn't adapt timber frame principles to use prefabricated laminated components, but you would still want to put them together with pegs or bolts.