Why are there so many wooden speakers?

The REASON to use wood is because any other option is WAY more expensive!   Sure other materials are used... and if you want them, you are quite free to pay for them!  
I have built 2 pairs of identical speakers (using 8" Tannoy concentric drivers), where the only difference was one pair used Baltic Birch ply, and the other pair was MDF.  The MDF's sounded markedly BETTER!  There was less... ummm.... woodyness, in the lower midrange.  I then proceeded to increase the internal damping of the birch ply with adhesive vinyl.  That helped, but the MDF boxes still sound better IN THIS CASE.  I'm not claiming that it's better for every situation.  For me to use any other material than wood would be extremely difficult and/or costly.   There is no wooden conspiracy as the OP seems to believe.    

@kenjit 
I wouldn't mind spending time with you discussing speaker design at some point.  Many of your arguments are valid, but if a manufacturer decided to build a no compromise cabinet,  very few could afford it.  I am grateful for plywood and mdf.  They allow me to build high quality cabinets that are affordable.  I have been very strongly contemplating going into manufacturing again.  I've been out of it for 35 years.  Just recently I've experimented with light weight concrete composites.  Vermiculite and styrene beads.  In the end, I have abandoned this idea.  In fact, I have been working with lighter wood products and using extensive bracing and deadening technics to built a very lightweight, strong and inert box.  It may not be as inert as I would like,  but I've done a few lightweight boxes that have produced very satisfying bass that can be handled much easier by an old geaser like me than your typical box..... It has been said all over.  Construction time,  Construction cost, Parts cost, time involved.... everything is a factor.  In the end,  The purchaser has to pay and the manufacturers are constantly juggling that cost vs selling price.  It isn't that a better cabinet can't be made or anyone wants to deny you.  I would suggest that you may fund a manufacturers development cost and I'm sure that you could get any type cabinet built that your hearts desire. Of course that isn't practical.... and practical is what this is all about.  Good Listening,  Tim (timlub)

I think our collective chains are being yanked by the OP, but the clever responses by folks far more witty than me have made this an interesting thread.  So far as I can see, MDF is an "engineered" wood product, but more immune to resonance issues.   Wood is wood, it seems to me, plywood of any composition included.  There are almost zero cost-effective alternatives so that is the simple answer to why wood is used in speakers.  

I had the oppty to hear a pair of Tannoy Westminster speakers this week, albeit clones, but employing the same birch plywood construction techniques as the real ones, with the addition of a wood-encased super tweeter, all powered by a very high-end tube-based front end.  Heck, if i had known that "wood" speakers were so tragically flawed, I would not have come to the conclusion that they were among the finest speakers my ears had ever had the joy of hearing.  

I did have a couple of pairs of Green Mountain Audio speakers, with enclosures made of a granite epoxy resin and they were excellent, but not intrinsically better than other wood speakers I have had, and brutally heavy.  I now have Spatial Audio OB speakers, which I think employ MDF baffles, and I have found them to be Holy Grail of speakers.

I had a pair of KHL Model 5 "wood" speakers a few years, recapped and re-wired, which were pretty sublime, with lots of balls in the LF driven by a tube amp.  I wish I had never sold them, a great "old school" sound, with a luscious mid-range response. Yet on my list of speakers to hear would be DeVore "wood" speakers, which garner tremendous praise and are the speakers of choice for many audio reviewers.  That said, I have heard many Harbeth speakers over the years that I found rather unmusical and drastically over-priced.   At any rate, it is difficult to imagine moving away from OB speakers for myself personally.    

Maybe you should just get planner type speakers and take the box out of the equation... 

Answer to O.P.: Because there are so many trees on earth. 

There's nothing inherently inferior about wood as a material for enclosures. There are certainly man-made materials with different damping/energy storage properties, but these often come with weight & cost issues associated. Moreover, there is no one man-made material I'm aware of that consistently makes a superior speaker enclosure, no matter who designs & makes the speaker.

Arguing the merits of different enclosure materials is somewhat like claiming that this or that digital chip makes a superior DAC: a helluva lot else goes into making a DAC, just as it does into making a loudspeaker.