While it is not common, it definitely happens – it's just often hard to find. Most sites offering it have it on their newsletter sign-up form, as a way of showing you what kind of e-mails you should expect. Like the Newsletter Archive link on Techsmith's site.
Balsamiq, on the other hand, doesn't have it, and indeed, they frequently remind you, both on the site and in the e-mails, that it is considered exclusive content: they even call it Inner Circle. Authors of such "exclusively-positioned" newsletters often even promise immediately accessible content (like you'll get this nice Fancy Tech cheat sheet) to convince you.
Other than exclusivity, and this shows in the naming and design of Techsmith's Newsletter Archive as well, is that many newsletters, at least partially, become obsolete quickly. To continue the example, Techsmith's newsletters mainly consist of links to tutorials and blog posts (both of which you can find on the main site in a much more convenient way than browsing the archive) and special offers on their software – which expire quickly, making them not only obsolete, but possibly hurting sales, as new visitors could look at them (if they were too easy to find) and think ah, this software was 20% off just two months ago, maybe I should wait.