It's not that the logo doesn't matter. It's that the specific shape of the logo doesn't matter. As long as it's unique and recognizable, over time it will come to be associated with your brand. As an example, think of car emblems. What does 4 rings have anything to do with Audi? The roundel with BMW? The bowtie with Chevrolet? Of course, these all have a historical significance, but there's no direct tie between the shapes and the name. It could just as easily be Audi's roundel and BMW's bowtie. But yet all are distinct visuals intimately tied to the brand.

Not much at all, or when you're bored, and have time to waste.

Does it look clean, professional and trustworthy? You have decent vector images of it? No negative associations? Just run with it, there's better things designer time can be spent on.

I think there's two reasons for changing it afterwards. It is starting to clash with the visual design of the site around it, and needs some touch-ups, or your company is moulting, and shedding it's past skin.