Need one a bit more dangerous than this.
Nah you need a surprisingly tiny mortality rate with a decent infection rate before secondary causes outstrip the damage of the actual disease. In the short term if you hit 5-6% with a high enough infection rate you are going to see people not go to work, shops shut, bodies waiting to be burned, that will kill off a few more people and the problem cycles again.
Long term if the disease continues cycling around the planet, mutating like a normal cold virus as it goes then the main damage will be economic - you can already see the market effect this morning. Economic collapse would kill the race way more efficiently than some wee disease.