No, you do not necessarily have to replace them. If you modify or stop overhead watering, use fungicides and keep clean sanitation practices, you can keep the plant and add other hydrangeas too.
I have two infested mopheads by the front door that were switched to drip irrigation decades ago as I applied new clean up techniques. They still have some leaf spots in late summer but not like when I bought the house. And other mopheads, paniculatas and oakleafs planted nearby have not developed leaf spot. While the fungus is almost everywhere, it is not as contagious as black spot in roses when you only water the soil, use fungicides and follow clean sanitation practices.
However, if one does not want to do those things, replace the plants.
For more info, see: The thread "Hydrangea problem"
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