Why is it Google's responsibility to administer all this? They have a published algorithm that is intended to maximize fair play on the web. If you don't like that algorithm find a way to buy off the other search engines for paid placement.
If you think that bias is a bad idea than Googles current approach seems okay. They don't bias against WSJ, but they don't bias for WSJ either - The Google bot has less material to work with, so their is less content compared to other sources, so it has a worse ranking. No bias.
They could apply a subtle background (like they do for sponsored results) to results that are behind a paywall, behind a registration-wall, or otherwise inaccessible.
- WSJ subscriber, where WSJ results should be present and maybe even get a ranking boost.
- User happy with paywall results, these results could be surfaced, with UI treatment indicating paywall.
- User uninterested in paywall results, where these results would be essentially removed.
The ranking between the latter 2 of these users could be a bit of a sliding scale too, rather than two distinct groups.