By describing the transformation of Alonso's body into stuff of the sea as "suffer[ing] a sea-change," Ariel is making an argument about the nature of transformation.
The first definition offered by the OED reads:
trans. To have (something painful, distressing, or injurious) inflicted or imposed upon one; to submit to with pain, distress, or grief.
Only much further down the list of definitions does OED offer a less loaded gloss of the word:
To be the object of an action, be acted upon, be passive.
The implication, then, is that the transformation is probably painful or disgraceful, or at the very least, passive and against the will of the transformed one. By choosing the word "suffer" to describe Alonso's experience of decomposition, Ariel inserts the image of pain, perhaps as an allusion to the Christian notion of suffering for one's sins. The word certainly implies a loss of power at the hands of natural forces, which unsettles the order Alonso set up for himself by disposing of Prospero.
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