The main reason I picked up an F2.8 zoom (the Olympus 12-40/2.8) was for low light performance.
I found that anything indoors, in the evening, photographing people, I needed an F2.8 or better lens just to prevent subject blur. Once your shutter speed gets to 1/30s or slower, your photos become slow enough that you'll start catching people breathing, causing them to be a little blurry, even though everything else is sharp. The slower your shutter, the more often this happens. By 1/15s, I found subject blur happening about 50% of the time, and nearly unusable for active kids.
To keep a reasonable shutter speed, you need either a high ISO, which introduces noise/grain in your photos, or you need a better lens, one with F2.8 or better, or you use a flash, which introduces a whole other set of issues.
Like most other photographers, I initially solved this with prime lenses, like the Panasonic 25mm/F1.4 prime, but after a while, I got tired of changing out primes all the time, and eventually bit the bullet to buy an F2.8 zoom.