Have to agree with the majority of comments I've read. I don't knowingly fund anything to do with News International, since I've been keeping up-to-date via the web for the last 10 years and via teletext in the 15 or more years before that, so as far as newspapers are concerned, only the free ones come into my home.
It's up to people to decide which causes they support and firms they boycott, and whether you consider they have no effect or not, OP, is frankly immaterial.
Try finding someone reading The Sun in Liverpool, and you'll find it very difficult (I don't think many newsagents even bother to have copies).
Boycotts by individuals may appear ineffective, but when one heard that at least a dozen advertisers had pulled out, and others were waiting to find out what their customers thought, it didn't take long for the decision to be made to close, because they knew that they could keep publishing but would have dwindling sales and dwindling advertising, and would just lose money until they pulled the plug anyway.
Taking the decision to close was one way to try to be "seen doing the right thing" but they even messed that up, because the chief exec was protected and the innocent (and not so innocent) staff paid the price.
You (OP) seem to feel that a boycott is bad because the employees will have it tough. Yes, in the short term, but the who are hard working and have been honest during their careers (ie not making up stories, the way some journalists have on some rags) will move on quite easily.