Would hurricanes on an ocean planet continue indefinitely?
No. As it is, many hurricanes never make landfall. In an oceanic world I could see three fates happening:

Hurricanes that dissipate due to dynamical features or climatological features.
By dynamical features, I mean things like two hurricanes that shear each other out or produce an environment that can't be sustained. An example of the latter is upwelling, which generates cooler water that saps the energy from the hurricane. A climatological feature that might prevent a hurricane from developing indefinitely might be the Azores high. As it is, there are places that hurricanes don't seem to go.


Hurricanes that undergo extratropical transition.
Notice in the figure above, the hurricanes just disappear near the poles? As they come closer to the poles, the temperature difference becomes larger. Eventually they no longer look like tropical cyclones/hurricanes (little to no temperature difference), but rather look like an extratropical cyclone (see this link for some differences). This process is called Extratropical transition.

Chavas and Reed (2019)
While looking up papers for this question, I stumbled upon this paper. It implies that we would get longer lived hurricanes spreading the entire planet. I'd be a little skeptical of this result though, since it ignores the fact that the earth is heated unevenly, which drives most of the climate.



On a side note, such simulations do exist. These are called Aquaplanet simulations. Some studies I found include:

Li et al. (2011)
Merlis and Held (2019)
Chavas and Reed (2019)
Viale and Merlis (2017)

And for kicks and giggles, if you want to consider what the worst-case scenario for a hurricane could be, such a thing has been named a &quot;Hypercane&quot; (see here, too).