Mostly agreed. Though your observations are mostly limited to the top tier of national newspapers. It isn’t as applicable to regional and small town periodicals. The liberal publications in those areas tend to be on an equal footing as their conservative counterparts.
That being said, the liberals dominate the news publishing (and broadcasting) business. There are far far fewer conservative outlets. So it is somewhat incomparable to make an overall observation.
Additionally, your example of the Wall Street Journal is a poor choice. The WSJ is actually a liberal leaning paper on it news pages (or at least it was until Murdoch bought it; it may have become slightly less so since, but it is still more liberal than conservative on the news side), though its editorial pages are famously conservative. Also, the WSJ is as well written as the NYT.