You'd use DW templates if you were building a purely static website with no interaction beyond following links. The template will allow you to make changes to the page layout, and all your pages will be updated to reflect the changes you made. You will have to reupload every page that uses the template in question, however.
As soon as you need more interactivity than simple navigation, or need to present data that changes over time, you've gone beyond the scope of what a DW template can reasonably do. When you get to that stage, you'll need some kind of server-side scripting language (PHP, Perl, Python, something beginning with P :) )
It sounds awfully like someone in management has heard that DW has templates and has latched onto that idea without really understanding what templates really are. Whilst it can be argued that they can improve performance in certain circumstances (a non-scripted web page will consume fewer server resources to run than a PHP script, for example), they aren't really suited to maintaining big sites, especially not if said sites require more interactivity/data presentation than DW templates can offer.