Yes, static analyzers mostly catch simple bugs. But it doesn't really matter if a bug is simple or complicated. You see, programmers believe they never make or make very few simple bugs: http://www.viva64.com/en/b/0116/

But they are wrong. They do make quite a lot of them. Here's, for instance, a bug database we have collected and keep updating: http://www.viva64.com/en/examples/.

Moreover, some bugs can take quite a while to find, despite being simple. Here's a nice example:

The conclusion is: the bug we had wasted about 50 hours to track was detected at once with the first run of the analyzer and fixed in less than an hour! Source: http://www.viva64.com/en/b/0221/

True, false positives aren't good, but they are not that much trouble. Static analysis tools provide numbers of means to suppress them. At least, we in PVS-Studio do have a lot of false positive suppression mechanisms. But it's a long story, so you'd better refer to the documentation.