I read on Neospirin's instructions that it is advised to apply only a thin layer of it. Why?
Like many medications you want to use the amount necessary, no more, no less. Contact dermatitis has been caused by Neosporin (and similar products). I would mention a few particular reasons:
Topical antibiotics can contribute to medication resistant germs, and having goop sliding out of a bandage and onto non-injured areas of your skin serves no beneficial purpose but does increase medication resistance.
The more you expose yourself to Neosporin-esque products, the higher your rates for contact dermatitis.
The effect of having a gooey half-Neosporin / half-body-fluid ooze coming out of your bandage isn't going to help anything, will weaken the bandage, and is spreading its little cocktail all over your skin.
In short it's pretty common to always use the smallest amount of pharmacology to achieve whatever ends. The more medicine you use, the greater the chance of side effects and the greater their impact will be.