Wrong! Of course the sway bar will move up an down freely when the bushing is worn and not doing its job. Think NVH (noise, vibration, harshness). It's considerably worse when a sway bar bushing is no longer gripping the bar.
When the bushing is worn, the bar will rotate easily, without being grabbed by the bushing, and will move laterally from side to side as well. Both those movements compromise the purpose of the sway bar system i.e. to counter sway and to dampen down the suspension. NVH
The bar has no collars on it to prevent the sideways movement brought about by forces on the sway bar when steering the wheels. That movement can be seen when bushings are worn.
The only thing that prevents the bar from doing what it's
not suppose to do (rotate loosely and slide loosely), is the grip the compression bond imposes between the bar and the bushing.
Compression bonding is a common type of sway bar system design, it doesn't involve lubrication maintenance. Chemical bonding, used on some systems, is another type. Are you saying a sway bar is free to move in its bushing with a chemical bond? The bushing bites it's teeth and screws up its face.

Compression bond and chemical bond both resist movement at the interface between the bar and the bushing. thereby affecting roll stiffness that a standard, free to move bushing design, doesn't. The free to move system design will also require lubricant, either by zerk or periodic maintenance of the lubricant (hard polyurethane bushings).
Sway Bar 101 from:
Sway Bar Bushing Replacement
1.
STABILIZER BAR WITH CONVENTIONAL BUSHING Note: Bar is loose within the bushing, decreasing the effectiveness of the bar. Also, the roll stiffness of the stabilizer bar with the conventional bushing is 17.7 N/ mm.
2. STABILIZER BAR WITH GRIPPY FLAT BUSHING
Note: Flat surfaces on bar and bushing to create grip. Causes stress concentrations.
3. STABILIZER BAR WITH UPSET RING
4. STABILIZER BAR WITH
CHEMICALLY BONDED BUSHING
5.
STABILIZER BAR WITH COMPRESSIVELY BONDED BUSHING
Take your pick. Which one is it? The installation instructions from both MOOG and Mopar, for the Vans' sway bar bushings, say "install dry, no lubricant", time after time. The Parts guys at Mopar are vocal about that, no ifs, ands, or buts.
By the process of elimination:
- no chemical adhesive involved, scratch #4
- no upset ring, scratch #3
- no grippy flat surface, scratch #2
- no lubrication required, scratch #1