The question covers most of it, but I'm trying to present a well articulated argument towards a senior developer who wants to abandon conditional stylesheets altogether (IE6, mobile, etc). Bear in mind we're not actually eliminating IE6, just the stylesheet.
Or am I being crazy and should just accept this?
You shouldn't. With enough work, both of the popular browsers can be made to render a page the same way. Take mine for example - Complex yet simple at the same time.
[edit: changed 'never' to 'you shouldn't', having thought the title said 'when']
If you can meet your needs without conditional style sheets, then by all means it's a good idea to have a single style sheet for all browsers. However, if you cannot do this without losing functionality, then a pretty good argument would have to be presented to justify going to a single style sheet.
What is the alternative? CSS hacks?
I have conditional stylesheets for IE7 and IE6. This compartmentalizes fixes for those specific browsers. When making changes, it easily lets you test/fix in standards browsers, test/fix in IE7, then test/fix in IE6. Testing flows more naturally. It doesn't break standards, it's easy, and it's basically free. It makes more sense to explain why you wouldn't use them.
You may want to look into the Yahoo Reset CSS Library. It has eliminated the need for conditional stylesheets on many of the projects I've done.
Because IE 6 and IE 7 are broken in various well known ways. Conditional Stylesheets that modularize the fixes are the easiest and supported way to deal with these breaks.
When you say your senior developer wants to "abandon" conditional stylesheets, what exactly does that mean?