I think timber was probably popular in the construction of bridges, say a century ago, because it's a material that can be sourced essentially near the site. There's no need to truck materials in. That might have been the primary reason why it was used then. The way to protect it was really the use of chemicals.
Bridges that are being built in Europe right now are built with a different approach. Basically we protect the timber from sun and water exposure through the use of a finish on the bridge. If you do that, the thought is that you can design a bridge for a 100-year lifespan.
The use of CLT, to address your question, is very appropriate for bridge design because it provides a very rigid deck element, which is critical in distributing wheel loads on a bridge structure. There are bridges being built with CLT right now.