Why isn't the UK, Sweden, Switzerland, Italy, ... doing this? Because it's a pretty strong form of controlled economy that distorts the market.
How would this work for search engines? Would you force people to use a different search engine than the one they want? (e.g. they type Google.com and end up redirected to Bing.com) ; or somehow just funnel revenue to other companies... then who gets to decide which companies this gets funneled to?
Anti-trust is about preventing anti-competitive tactics, but the scheme you is ironically anti-competitive: it artificially inflates usage of other services even if they don't provide an equal/superior service, with consumers paying the price.
[disclaimer: I work at Google, so likely biased]