As for fairness: loser pays disincentivizes bringing lawsuits, whether meritless or meritorious. Under loser pays, certain frivolous lawsuits would not be brought, but meritorious cases that are often uphill battles would not be brought either. If you're in the business of going after polluters (like the Sierra Club), or challenging national security policies (like the EFF), the law is not on your side, even if your cause is just.
As a practical matter, you can't just take the English rule and import it into the U.S. Europe is an "ask for permission first" place, while the U.S. is "ask for forgiveness later." That allows U.S. companies to move faster, but puts the legal system in the position of being a backstop for unsafe products, financial fraud, pollution, unfairness in hiring, etc. So for example, it would be unfair to make it untenable for individuals to bring lawsuits for wrongful termination without giving them the protections against arbitrary dismissal European workers enjoy.[1]
Much of the support for loser-pays in the U.S. is an attempt by businesses to have their cake and eat it too. They don't want plaintiffs lawyers' bringing privacy lawsuits, but they're not exactly clamoring for that system to be replaced with European-style data protection laws administered by regulatory agencies.
[1] Which model is more efficient is debatable. I think in areas where causation is difficult to prove (environmental, product safety, employment discrimination), "ask for permission first" does a better job protecting the public at lower cost. But it also gives tremendous additional power to the government to micromanage the economy.