The article mentions a budget of a billion DKK. This would be a bit over 100M $. So, expensive but not that outrageous.

Populations on these islands and their economies are small precisely because it is hard to get there and requires operating ferries (which costs money as well). Solve that problem and you might expect to see an effect on the local economy (more tourism, cheaper to move goods around, commutes to the mainland, etc.). If you then consider that they'll be benefiting from this for decades/centuries, it suddenly becomes a wise investment.