How fast can a hand spinner spin?

This is a question that has several answers.

For woolen, even a simple drop spindle will insert twist faster than most treadle spinning wheels. If you are looking to spin woolen yarn at 5,600 ypp, and willing to work very hard, a drop spindle with a very thin shaft and removable whorl is fast.  Most people do not spin that fine, and lower grist yarns need less twist and more ability to handle the produced yarns.  If you are spinning a 2,000 ypp woolen yarn, a wheel or e-spinner works well, and will be faster than a drop spindle.

The big deal is worsted. I have no idea how fast most modern spinning wheels  (single drive, flyer or bobbin lead) will produce worsted. Most modern "double drive" wheel are really single drive wheels with a complicated belt tension adjustment.    

Most modern treadle wheels have large amounts of slippage at the flyer/bobbin assembly whorl, and thus the ratio between the drive wheel and assembly whorl is not a good estimate of the actual rate of twist insertion.  However at high rates of twist insertion (greater than 2,000 rpm), without true DRS, it is essentially impossible to produce a high quality thread with uniform twist.

Great wheels are faster than most modern treadle wheels for woolen thread. They will produce woolen thread as fast as a drop spindle at less effort. They will produce worsted thread faster than a drop spindle but it is a difficult, high skill activity.

I have a true differential rotation speed (DRS) double drive wheel. For what I spin, it is far and away the fastest method of hand spinning yarn that I know.  It will spin 5,600 ypp worsted singles at at rate of 560 ypp, or about 400 yards of 5,600 ypp woolen singles per hour because I put more twist into my woolen yarns. I can spin 8 hanks of 10s per day. It will also produce worsted 11,200 ypp singles at ~ 400 yards per hour. 560 yards of 11,200 ypp single weighs half an ounce and takes me about 90 minutes to spin. That starts to be real work, I would not plan on more spinning more than 4 hanks of 20s per day. My wheel will produce 24,000 ypp worsted singles at about 350 yard per hour. It will produce 43,000 ypp worsted singles at about 100 yards per hour. A hank of "fines" weighing 6 grams will take me most of a day to spin.

 I never spin more than about 2 ounces of yarn onto my spinning bobbin, because with a higher effective diameter bobbin, my DRS system become less effective and yarn quality goes down. Regardless of the grist, I spin a hank (560 yards) and wind off.    

Your mileage may vary.