Does the subwoofer have to be on the floor?

I can remove drawers, but I will still have a shelf underneath that I cannot remove. For that matter, I think there is some hollow space between the shelf and floor. Would simply removing the drawers be good enough? I do not understand what the big deal is anyway. Regular speakers can have stands, why can't the bottom shelf, which is very solid, act like a speaker stand?

...the hollow space is not a big deal and you can use it, but since sub has a large flexibility of placement i.e. can be realy away from the mains or somewhere in the middle of room or under the journal table or even under your desk.

Its usually bad to put a sub in any cabinet. Just like it can be a problem putting a sub in a corner. Not only will it shake what's on the shelves, you will get resonance problems (you are putting it into another box). The only way around that is with an equalizer.
Can you put the sub on top of the cabinet? It may be more open up there?

Some subwoofers are designed to be placed close to the floor so that floor reflections can reinforce their volume. I suppose you could adjust the volume control to compensate.

A proper location for the subwoofer would minimize excitation of room resonances. Most installations achieve this through either a room resonance calculation or trial-and-error -- moving the subwoofer around the room and listening for resonance excitation. A location selected based on decor considerations would be appropriate only through coincidence.

The support structure may have a resonant frequency within the range of the subwoofer's operation. This could cause sound coloration, as well as potentially disastrous destabilization of the structure and/or its contents. To your point, most speaker stands are designed to have their characteristic resonances out of the speaker's normal operating range, or the stands are so overbuilt that they remain resistant to excitation by the speaker. Perhaps your cherry shelves are likewise sturdy.

I have subwoofers in enclosures in two of my setups. In one, the subwoofer is on the bottom of a very solid wooden cabinet, open in the front. Since the subwoofer has two sidefiring radiators, I need to leave a good amount of space on either side of it or I can hear some coloration. I haven't had a problem with vibrational stability for the cabinet or its contents. The other subwoofer is on a built-in bookshelf. On occasion, I can hear something rattling on one of the shelves. I have hunted down most of my rattles and padded them away. Needless to say, neither of these is really recommended in an audiophile context. I'm not proud.

My key goals are to be able to enjoy the low notes at volume and to blend the subwoofer range in with that of the other speakers. The latter is difficult to achieve, and the more constraints placed on the subwoofer, e.g., limitations on locational flexibility, the harder it is to attain. Good luck.

You should look at building a passive sub into the cabinet and amplify it exteranally. Use Liquid Nails on all screws when you put it together.

I had my sub on a brick fireplace 5" elevation and it sounded aweful (lack of energy) it was a VMP with a Slot loaded passive (probably part of the problem)

Another option
Chris