It depends on the venue. In computer science, it is often possible, but there are often weird restrictions: embargo delay, only the preprint, must include a link to the publisher version, only on a personal webpage or on certain kinds of repositories, copyright assignment has been signed as well, etc. So you don't always feel comfortable doing it.

Further, we academics are incentivized, in terms of career, to publish in prestigious venues managed by official publishers. We aren't incentivized to publish in open access repositories as well. So, even though most of us want our articles to be disseminated widely, not all of us can find the time to make sure that the paper is also available on an open repository. This is a factor that explains why many articles are not available for free online even in cases where it would be legal for researchers to upload them.