Could you imagine how nice it would be to have the wood pressed into a single panel like like the tesla gigapress. I realise that it would have its drawbacks, but that wood paneling would look sublime.
There is a product called Richlite which is essentially the process you mentioned. It starts with dyed paper pulp that is saturated with resin and then compressed with pressure during curing. The appearance is not very wood-like but very "modern" and it is a very expensive material to purchase panels. It is very heavy and a monolithic material approximately 1" thick.
The more common industrial process is material called "high pressure laminate" which is your standard countertop laminate material that's only 1-2mm thick and is glued to a cheaper wood substrate.
Wood actually has some properties that make it desirable in a fire: the charring creates a natural barrier and it doesn't melt meaning it holds structural integrity. This makes it very desirable for building construction, but for cars it means it can act as a fire barrier potentially, and save lives.
