Actually there is another reason for putting sites on another IP. I do this for many of my sites so I can have all of a reseller's sites running under one IP. This is useful to lower DDOS risk for instance, if baddies DDOS that IP and we have to null-route it only that reseller is affected. It is actually also possible to setup exim so that email for a particular domain, or group of domains, goes out on a different IP, although you'd have to do so manually. It can also be used to facilitate transfer to another server.
For a related reason you should never make your main shared IP be the same as your server base IP. The reason for this is that if your shared IP is DDOSed and subsequently null routed the server won't be accessible via WHM, and possibly not available at all due to the way some datacenters handle their VLANs. Also cpanel licencing won't be able to call home so your cpanel installation won't work at all. Makes it really hard to fix things/determine the DDOS target!
As for the competition grabbing a list of sites on your server, moving them around isn't going to help, heck i can pull a list of all domains using your name servers quiet easily.
If nameservers are secured correctly, this isn't possible via zone transfer (that is, if an access list is used, as should be.) Regardless, Shaun's point still stands, as there are multiple providers out there who can tell you how many domains are hosted on a site/particular IP based on access to domain registration data and analysis against nameservers (whois.sc is one I think).