If you install an S trap, you might as well not have one.
The p-trap will siphon itself dry and smells from the sewer will be in your home.
You will have defeated the purpose of having a trap.
A better solution may be to cut the wall and move the tee in the wall higher.
Or cut the drawer.
On the shutoff near the floor. You can either cut the tile, or cut the escutheon.
It's just a looks thing, no real reason to have one except for looks. We sometimes have to remove them anyway.