It's not about whether I like an expression
Very clear? I think not.
Under your definition, if I write 'reduced it by a factor of two-thirds,' readers will think I mean 'multiplied it by 3/2, making it 50 percent larger.' Do you seriously believe anyone will think that? Is that your intent?
Under your definition--but not under mine--to 'reduced unemployment by a factor of zero' would be impossible, since you can't divide by zero.
Under your definition, if you leave a value unchanged, you're reducing it by a factor of 1 (100 percent divided by 1). by your definition, reducing by a factor of 1 = increasing by a factor of 1 (100 percent x 1). That's jarringly counterintuitive.
Under your definition, if you reduce unemployment by 1 percent, you're
reducing it by a factor of 1.01 (since 1 divided by 1.01 = 0.99). Not at all obvious.
I completely agree with you that journalists who write 'increased by 1%' when they mean 'increased by 1 percentage point' are guilty of ambiguity and worse: stupidity or contempt for accuracy. Ditto for journalists who write '3 times greater' when they mean '2 times greater' or '3 times as great.'