NOT using loadable kernel modules could increase security. Is this true?
Yes, but so will ripping out your network card and filling all your IO ports with epoxy. However, I don't think you want to do that.
Depending on how you define it, most modern operating systems have dynamic kernel modules. I think Windows kernel-mode drivers qualify as do Mac OS X has Kernel extensions.
The sad reality is that while kernel modules/extensions/drivers have vulnerabilities, your computer is far more likely to be compromised by using the same username and password on your local machine that you use on [facebook, google, stackexchange, etc], or not turning off a remote access service like tftp, rdp, ard, ftp, WebDAV, etc. There are certainly plenty of security issues on standard commercial computer systems, but I would make sure I had fixed the more commonly exploited issues before looking to rid my system of dynamic kernel modules.
Yes, some companies actually do this, see Pod Slurping: additional measures, Securing USB Ports, and Acceptable Use Policies: paragraph 6.