It seems that nobody has pointed out the third advantage of capacity
hats; that they reduce the Q of the antenna, and therefore broaden the
bandwidth.

If we define bandwidth in terms of 3:1 SWR(50), a capacitive hat tends
to decrease the bandwidth since it reduces the feedpoint impedance. For
instance, the 3:1 SWR(50) bandwidth of a 1/4WL vertical is about 1.2 MHz
while the 3:1 SWR(50) bandwidth of a 1/8WL vertical with horizontal top
hat is about 0.5 MHz according to EZNEC.

What would be the 3:1 SWR(50) bandwidth of the same 1/8WL vertical,
with no horizontal top hat, under the same conditions?

Actually I guess there would be two sets of conditions:

- No base loading coil or matching network (in which case I'd guess
it's outside the 3:1 range anyhow)?

- A theoretical (but handy) zero-loss matching network at the base,
giving it a 50-ohm feedpoint impedance at the desired center
frequency?

I think the latter is what was being referred to by the original
poster.