Well, unless it has changed in the last few years, they had far more influence than you are suggesting. I know for sure that they issue "preaching subjects" that SB Pastors are expected to preach on each Sunday. I have seen the Pamphlets/Letters they send to Pastors a friend of mine used to get. They have a distinct "message" concerning each subject preached on, and the Pastor is expected to follow SB Teachings on each subject.
The Council or Convention also decides what "theology" will be preached/taught in SB Churches, and Pastors are not to deviate from said "theology."
Their Tith requirements are certainly enforced by each Congregation, as is the Letter of Membership they require for each person in the Congregation. I saw one man and wife fill out a Form where they had to list all of their sources of Income, properties they owned, and assets, and were expected to tithe based on such information. If they failed to do so, once would get a friendly question, twice would get a friendly conversation from a Deacon, three or more times could end up with two or more Deacos visiting them and conversations about their being in danger of having their "Letter" pulled from Membership in the Congregation.
This is not fiction. I know two men and their families that were put out, given their Letters back, because they refused to tithe what they were expected to.
As for Warren and Saddleback, I could not care less, I have never agreed with his teachings. But the NC Mega Church is a far different story. Regardless of ones views, losing several thousand "tithing members" is going to have an effect on any Organization.
As far as "cleaning house," well, yeah, I guess one that agrees with SB Ideology would see it that way......
Anyway, the Article speaks for itself......... I think there will be more dominos to fall as the SBC "cleans house." But, who knows?