As I am sure many are aware that the H1 tag is an extremely important part of the search optimisation process, in particular when working with Google. I would go as far as to say that it would be in the top five of the SEO strategies to be put in place on any site. Without a H1 many of a sites pages simply will not rank in a high enough position to generate traffic. Google and many other search engines use the H1 to determine the main subject of a page much like a person does when browsing a news paper. If a H1 is not present we force the search engine spiders to go looking in other places on the site which are less controllable.
I also believe from site usability testing that a site visitor finds comfort in seeing the words they have searched for stated directly on the page, as it implies the page is highly relevant. Seeing as the H1 plays such a large role in the optimisation of the site pages it is highly likely that the term a person searches for will be found on the landing page that they arrive on in a large text H1. Internet users are consider time poor and will often give a site page less than a few seconds before deciding if the page they have landed on is relevant to their search or not, again the implementation of the H1 can reduce the bounce rate of site by immediately revealing to the visitor in most cases the keyword term they have used.
Aside from all this I personally think that if placed properly the addition of the color matched H1 on the site header is aesthetically appealing.