Hey Rob,
Let's take a human angle at the h1 tag. It symbolizes "heading". Heading to a piece of information which can be an article, a blog post or company intro/product description on a website.
It's a very very common practice to give a heading to any information that we (humans) want to present. It's very natural and meaningful too as it tells our readers what to expect.
This is probably why search engines give importance to h1 tag(main heading), they are trying to think like humans do, to determine the relevancy of a certain page to corresponding search query.
Similarly alt text gives them an idea that the image is relevant to the subject talked about on the page.
So, I hope that explains. You should continue to avoid using image in h1 tag.
Write a nice compelling heading for your human visitors then, for search engine spiders, wrap it in h1 tag and use your main keyword once (if it isn't there naturally).
Hope that helps.