The basic metal frame that you usually use with a box spring and mattress - can you substitute plywood for the boxspring?

I don't want to put my daughter's new 'big girl' bed on the ground (her room is really really small and we need the underbed storage space) but if I use a frame, boxspring, and mattress then she will be able to climb up onto the window ledge (like a window seat, but about kitchen counter height above the ground.

So, I need the frame, and I obviously need the mattress, but how important is the box spring? I read in another post that as long as the mattress had adequate support there wouldn't be any problems. Is there something I might be overlooking?

Any other ideas? One of the reasons I am anxious to move her out of her (converted) crib is that she uses it to climb up onto this window ledge. I have visions of her doing a header off of this some evening...

Jen in Okinawa
Mom to Noelle (2 1/2)