No, it's not normal. Although the potential is always there for the root file system to end up corrupted if the power is suddenly cut, the chance of this leaving the system unbootable is pretty small. In 15+ years of linux and ext2/3/4 use, including perhaps hundreds of power kills, I can't remember seeing it happen, or at least, not to the extent that a simple
fsck didn't fix the problem. That includes the pi. I agree with joan that you should avoid doing this, but I admit that I regularly pull the plug when I've screwed something up with a headless pi and am simply too lazy to get a screen and keyboard,1 and I occasionally let them die on a battery.
However, most of my power kills have been arbitrary on a system that was likely idle at the time (literal power outage), or else because the system locked up to due to either driver bugs, kernel experiments gone wrong, fork bomb style out-of-memory problems, or I/O errors on a storage device that was broken. Under these conditions the filesystems would probably be synced after a few minutes. Point being, I haven't seen it happen to a extremely busy but properly functioning machine very often.
There do seem to be a handful of people who report peculiar problems like this here. They repeatedly end up having to repair the filesystem or re-flash the card. Make sure the image you are using is relatively recent (2015); there may have been a kernel bug from 2013-14 that could produce arbitrary corruption.
There are even people who've reported corruption using a read-only file system, which implies that some pis have an electrical problem with the SD card. If the chance of this happening were increased when the card is busy and the power is pulled, it would explain why some people are plagued by this kind of problem and other people never encounter it.
1. Here's a suggestion about how to deal with that if it happens to you a lot.