<p>I'm trying to make the case for click-once and smart client development but my network support team wants to keep with web development for everything.</p>

<p>What is the best way to convince them that click-once and smart client development have a place in the business?</p>

They have a place in the Windows environment but not in any other environment and so if you intend on writing applications for external clients, then your probably best sticking with Web based development.
I heard this "Write Once, Run Many" before from Microsoft when Asp.net 1.1 was released, it never happened in practice.