It's more efficient to remove the cause of emissions than to tax it and try to compensate for it. All carbon emissions should be taxed, but some things should just not be allowed.
Of course, it could be that the C-H bonds contribute much more to the energy released by burning the fuel than the C-C. But this doesn't seem to be case. Here's a paper in favour of switching to lighter fuels for ships: it argues that the total supply chain CO2 contribution would be higher (it takes energy to refine those fuels), but only by 1%.
I think that "bunker fuel is really bad and ships switching to lighter cleaner fuels is important for the environment" is a seductively easy but bad target for carbon reduction. There are way better places to spend our efforts.
[0] https://www.tandfonline.com/doi/pdf/10.3155/1047-3289.58.4.5...
The easiest, most economically efficient, most productive way to do it is to tax the C content of fuels. Use the monies raised to subsidize green energy.
Banning is an indiscriminate club that does a lot of collateral damage.
The regulations we have now (no high-sulphur fuels in cities, no leaded gasoline...) are better than taxing only CO2 emissions, even if they're not perfect.
The problem with banning is its inflexibility. For example, let's say you have a bunker-fueled emergency generator for a hospital that you use only when the power goes out. The pollution it emits is negligible. But by banning bunker fuel, you'll have to replace the emergency generator, at considerable expense and environmental cost.
With taxes instead, you:
1. bunker fuel will only be used when there's high value for it, and you won't have to add a plethora of exemptions into the regulation
2. have a revenue center for the government instead of a cost center - revenue that can be used to subsidize green initiatives