Thinking about this again and I realized. Light had the Director commit suicide. He wouldn't write his father's name, but if placed in a situation like this, Soichiro would not hesitate to sacrifice himself.
If Mello kidnapped Soichiro, he might genuinely think Soichiro is under the control of Kira. Keeping him alive is a Odyssean task, the results of which could shape the entire investigation.
Scenario A: Soichiro is successful. This narrows the suspects to the task force who kept the kidnapping on the down-low. Light is fucked over through no fault of his own.
(This could be prevented if Light, aware since Yotsuba that his father is Like That, makes it public specifically to cover his own ass. Either the kidnappings get increasingly ridiculous, or the mafia doesn't get the notebook.)
Scenario B: Soichiro is unsuccessful. The investigation goes back to the first time he had a heart attack, when L questioned was it possible Kira tried to kill him and failed. This does immeasurable damage to the collective understanding of the Death Note. Light is thriving.