I don't think that it would be a good idea to change h2 -> h1
An h1 tag should appear only once in a site that is why it is usually used for the site name or logo.
An archive or category page would list a number of h1 titles which would result in incorrect html structure.
There is some evidence that h1 weighs less than h2 tags
Ben Pfeiffer from ranksmart.com
Keyword Use in H1 Tag
Not as important as it once was as a ranking factor, but still necessary on a well optimized page and very useful for organizing page content.
specialist Thomas Bindl
Keyword Use in H2, H3, H(x) Tags
2nd most important on-page criteria (weight changes every now and then and it can happen that h2/h3 have the same/higher importance than h1