Not physically, no. You're right, that would be horrendously uncomfortable. However, there is a documented history of witches using such things as flying ointments, and taking spirit flight into the night via the broomstick, stang, and distaff. I believe at one point in time I even read about a witch using a ladle (can you imagine?)
As far as the brooms provided here, I haven't seen them in stick for quite some time. You might want to try googling the process of broom making, as it is quite a fun process (speaking from experience), and very rewarding. You have sand the shaft, carve it, stain it, leave the bark on, really anything that feels right to you. Then you attach the bristles, and you've got a broom. I'll tell you, there's nothing quite like looking at a tool you've made yourself, and knowing it's absolutely yours in every way.