What I do a lot in the Summer times is to slice water melones. At this task, wider edge means awkward; but thicker edge means impossible (the melone peel simply crashes). So, thick knives can cut like thin knives (sharpened at the same profile) only if the cut doesn't involve deepness, if it doesn't require the knife itself to traverse through material.

However, regarding thin knives, not batoning is what I'm concerned about. I have a one millimeter thick blade which batoned through bones for many years, hammered into the spine and never had a problem. But the problem with thin knives is that they can't chop and can't pry. For me, for a multi-purpose knife, the ideal thickness is 4 millimeters (which means 1.575 inches). Otherwise I prefer thicker knives because their advantages seem more important than their dissadvantages in my use:

Advantages of thick knives:
- they can chop better being heavier
- are stronger for batoning
- thickness is an advantage for splitting wood
- have more lateral strength which grants the possibility to dig into the ground (even in rocky soil) or into the wood (even hard wood)
- you feel more confident if need to use it as a weapon

Dissadvantages of thick knives:
- are awkward for slicing when it needs to traverse the material
- are more difficult to regrind when consumed during repeated resharpening
- are more difficult to carry being heavier
- are more banned by police because they look stronger than kitchen knives.