I have that exact stand bought from Benjy on SMF and it works well, the forks are able to be bent in and out to suit your preferred brush size and if you prefer to hang at the top of the handle (as your picture shows) or where the bristles meet the handle, it is quite nice in the flesh and got the royal seal of approval from the household management.
I like it but I do not believe it helps at all in any practical way. I might seem daft to spend money on a stand if you do not think it does anything, but it looks nice and it holds the razor and brush I used that morning. This saves me trying to find a safe place for the razor every morning and the wife and daughter leave it alone. If it was left loose on the counter or lying in a cup they would move it, possibly cut themselves or knock it over.
I have tried drying my most densely packed brushes both hanging and standing up and found no difference in time to dry. I think standing bristles up does no damage, at least in the short term. I really doubt there would be a long tern impact either, I think using the same brush every day is worse if it never gets any time to be 100% dry (or very close to it).
If you like it buy it, swmbo will like it and you can tell her it is a brush dryer and everyone is happy.