If algae otherwise could be coaxed into yielding passable efficiency to a fuel process, the growing sensitivity of the algae probably would be the least of our worries.
I don’t think this could really take off until we came up with an algae that thrived in the saltiness of ocean water. The expense of furnishing it with fresh water would be prohibitive.
There are many species of algae which thrive in salt water. In fact one set of them, blue green algae, might have advantages. These can survive in a higher saline environment, so a tank could be created which could not be contaminated by other species. However a highly saline environment is also highly corrosive, and so expenses would rise.