My latest insane theory: I don't think that Jack having Irumodic Syndrome is just for drama with his father.
Perhaps the morphogenic virus was based on Irumodic Syndrome (perhaps even with samples using Picard's DNA). These Changelings could have either contracted a mutated form of the virus (the cure was based on the source, Odo) or perhaps they found a way to use the virus to improve their abilities even more but it's gone wrong. I think their plan is to use it to help themselves but also develop a virus to attack the Federation.
Better samples are needed for their plan, which is difficult due to the rarity of the disease. They stole Picard's body but discovered a corpse wasn't good enough, but managed to use a database to scan for signs and discovered Jack.
In short: I'm not entirely sure why, but I think Irumodic Syndrome is very important to the overall plot.