The eye provides a natural constraint over a storm's intensity. Inherent to hurricanes -- other than the intense but steady-state and rare annular storms -- are the eyewall replacement cycles. An inner eye can only get so small; if it were to contract to a small enough radius, the necessary subsidence in the center of the storm to keep it in balance -- as manifest by the eye -- erodes, throwing the storm out of balance and ensuring a weakening cycle to come to account for the imbalance. The eyewall replacement cycles are a way to maintain this balance, replacing the inner eyewall every so often and repeating the intensification/weakening scenario again and again.
Further, hurricanes are like a Carnot cycle of limited efficiency; they are only as efficient as the environment will let them be. The maximum potential intensity formulation (see http://wxmaps.org) provides an idea of how strong hurricanes can be under such a cycle when taking into account sea surface temperatures and temperatures at upper levels, a maximum that is very rarely exceeded, and probably provides the best representation of what you are looking for. But do remember, the majority of storms do not come within 20mb of their MPI -- and most are even further away.
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