That's like saying don't use HTML if you don't want any images. There's absolutely nothing wrong with removing the weight of the font from those elements. They're still two or more times the size of non-heading elements in the same container by default.
You use H1 and other headings in the name of semantics to help visitors and machines (google crawler etc.) to better understand the essence of that page. Not visual effects at all.
The font weight of bold can look pretty crappy. You can still make it look nice and an official header if you use a large font size. I have some headers on size that aren't in bold, but in a large font. Sometimes it's necessary for graphic design and balance of a page. The whole point of css and styling is so that we don't have to stick with default settings.
Text looks pretty crappy in general. I took mine a further step ahead: <li class="h1os"> <-- header image <h2 class="hidden">Open Source</h2> <h2> hidden for SEO example: orici.net Theres a new technology called sifr where you can replace the default text. Features different fonts that are also perfectly aliased through flash.
Eh, it's not that new. Flash Image Replacement has been used regularly on several pages. It's a big slow, but is nice for showing fonts that the user is unlikely to have. Deathshadow is developing a CSS/Js version of letter image replacement. It'll be nice if that can be another alternative. Or you could just use normal image replacement. http://www.mezzoblue.com/tests/revised-image-replacement/