I do.
I’ve been riding balsa boards or boards with 3-6" of balsa stringers almost exclusively for 15-16 years.
While many surfers believe the weight of the balsa boards is what gives them momentum, I believe it’s as much the stiffness of balsa.
A couple of anecdotes that brought me to this conclusion:
1980 or so. I was on Kauai for a couple of days doing sales calls with the Sundek rep there. After a day of visiting stores, N, Yoneji Store, Ching Young Store, Joe Kitchen’s Surf Shop, I returned to the Kauai Surf Hotel to find some nice little peelers on the right side of the cove there. The South Shore was out of control and there was a bit of a swell sneaking in there.
I’d left my board on Oahu. The beach boy had some boards for rent and I opted for a 7’0 Morey Doyle soft board. I paddled over to the break (only a couple of guys out) and paddled into a nice little wave, faded left and cranked the hardest turn I could. Half way through the turn the board just collapsed. It went all springy on me and died.
I flashed back to some experiments at G&S where I was working 10 years earlier. Skip had made a flex tail. He’d ground the foam off of the tail of a board from the top leaving a glass only tail for the last few inches.He was looking for flex. I don’t remember the details but he never made another one.
About the same time, Tom Morey had stopped by in his 1950 Chrysler business coupe and shown us a trunk full of spongy boards he called “Water Snakes” with s.n.a.k.e. being an acronym for something. Of course these later became the “Boogie Board”. Larry Gordon took some of the foam and then took a stock G&S board and ground out the top of the board removing most of the PU foam, leaving the fiberglassed bottom intact. He added some boogie board foam to fill up the board to the deck line. The board was comfortable to lay on but it didn’t ride very well. Too much flex.
A couple of years ago I was surfing “Threes” at Waikliki on this board:

I took off on a wave just behind the peak and at the same time another surfer took off right in the peak. We both went right. When we got to the end of the wave and both kicked out he said, " Wow, I’m sorry. I didn’t think you’d make it around that section". I laughed and said, “I wouldn’t have if I hadn’t been on a balsa board”. I let him try my board.
Later on the beach he ordered a balsa board and one year later he’s riding it. Now he’s taking off behind the peak. 
I think Thrailkill hit the nail on the head with his comments above.If your flexi flyer is chattering along you’re losing forward motion. And yes, there’s no doubt that flex, either in board or fin will delay the boards reaction time. I’m not saying that’s bad if that’s what you’re looking for.
I remember Skip Frye sanding his fins until they flexed to his approval. He would go into a turn and load the fin up and then when it sprang back it would launch him out of the turn. I have some old movies of him turning that way and you could see the results of how the fin was working. I remember him trying it with the plasic w.a.v.e. set fins. I was there the day he threw the gym bag full of plastic fins in the trash can in front of the P. B. Surf Shop when he went back to glass fins. So it’s not just flex. It is the return. And that has to do with the materials.
I’m not saying balsa boards don’t flex, but under most conditions they don’t and if they do the spring back (even on foam boards with balsa stringers) is quite different.
I remember reading somewhere that Dewey Weber discovered back in the early sixties that a foam board with a wide balsa stringer would have some riding characteristics of a balsa board.
When the first foam boards came out in the late fifties they were called “flexi flyers” and wood was added to make them stiffer (and to retain rocker).
It’s wood that will stiffen a board up more that any other factor.