I would take it from the other end of the question:
Is it possible for a knife to be too sharp?
My answer is: No.
That depends. If I sharpened one of my larger fixed blades down to a very acute edge (like a straight razor) it would do fine with shaving, slicing paper, ect. However, the first time I use it to chop/baton or do any other hard use, the edge would become useless. Probably broken, bent, or heavily chipped. How sharp a tool needs to be depends on the application and what the design/materials can take.
I think your confusing sharpness with the angle, and grind profile, which the blade is configured to.
Edges exposed to more impact and used on harder and tougher materials are usually better sharpened at a more obtuse angle and the grind will typically be one which better supports the edge more.
A straight razor is sharpened at a fairly sharp angle and the grind is often 'hollow ground'. The angle means the edge slices the hair with little resistance and the grind keeps the supporting metal behind the edge out of the way of the cut to reduce friction. A hollow ground blade also sharpens more quickly because you have to remove less metal to reform the cutting edge.
The down side of a hollow grind is that the edge is very much sitting out there on its own unsupported and unprotected from lateral forces or impacts when contemplated in cross-section. Straight razors are rather delicate. So much so that simply dropping one in the sink can break off chunks of the edge and require the razor to be reground at the factory. It is hard to find people who know how to regrind and retune straight razors so the cost and shipping can be prohibitive. Dropping or otherwise abusing these units can mean you need to buy a new one. Not very cheap if you buy quality.
A meat cleaver would be ground to much less of a fine angle and usually to an 'axe' grind that effectively surrounds and supports the edge as it absorbs the stress of impact into hard materials.
Neither the angle nor the grind define how sharp a blade is. Sharpness being how mathematically precise and smoothly the angle of the edge is closed.
A knife used to split wood by being hammered on or otherwise being used roughly in tough materials would benefit from a more obtuse edge and a more supportive and impact resistant grind. If your going to use it like a splitting maul it would be best if the grind and sharpening angle more resembled a splitting maul or axe than a straight razor. Once the blade is well configured it would be better if the edge was appropriately sharp. A different issue.