Custom CSS for home page.

How about CSS Injector?

You can just use the .front class in your regular style sheet. That's what I do. It won't really matter because global is going to load anyway, and once loaded it's cached so it won't add extra load time to subsequent pages. The only issue I see is if they are externally referred to your site, and never see the home page, they are loading the styles for nothing, but unless you have a very very style-rich front page I don't think this would have any real-world impact.

I wish context module (or something like it) could do this.

Well Delta and Contexts can do it. You just make a Delta of your theme and configure how you want the home page, then make a Context and say based on path change the Delta to the one you made.

It's just overkill for this, usually. But it depends what you're doing.

I suggest you to Use Panels.
It allows you to add custom CSS from the panel itself.

So I just did this using Delta + Context on my latest project. My front page is basically a delta of my Omega theme setup that uses it's own zones and regions that are not used for any other pages. So now that I have unique zones and regions I can have unique css for those zones and regions. It sounds like overkill because of everything else you can do using this technique but it's actually not very hard to set up. My only concern was how much overhead it would add to the site but it doesn't seem to have much effect.

I'd say give it a shot. Knowing how to used Delta + Context with Omega is an important tool to have anyways imho. A very powerful combination.

Would still like to see something like this added to Context so that Delta would not have to be used.