Do different speaker stands can really make a big sound improvement?

Speaker stands make less difference than cables and those make ZERO difference. Do the math (your bank account is debited with no sonic benefit doesn't sound wise to me).

Think….of course ! The direction of your sound is travelling along the floor if that’s where you now have them. Makes sense to have it ear level at a minimum don’t you think ? And filling with sand great idea if you’re a weightlifter, depending on speakers makes absolutely no difference. 

All speaker stands have a pronounced effect on the speakers presentation. Some speakers work better with low mass stands and others with heavy high mess stands. Unless there is documented results from users as there is with Harbeth speakers, it is a matter of experimentation with your particular speakers.

In a good system, any changes will make a noticeable difference. Be it speaker stands, rack material, type of spikes or never spiking, AC outlets, even the wall plates, type of room your system is in, and its acoustics with treatment (best bang for the buck) not to mention power cords that can make as big of a difference as a new piece of gear. Then of course all types of conditioners will change the sound, as well as the room temperature and humidity, so the more complicated your system the more factors you finally hear when sitting down and listening to your system which is why any reviews are only an opinion of what that speaker or gear sounded in that room with their gear etc. TAS does not exist, what does is the sound and taste of the coloration that makes your system so enjoyable.