If you think the barrier to entry in the search market is low, you should have a talk with Yahoo or MS, both of which have spent a billion or three on what you call "almost nothing". Either they're all idiots, or you're missing something.
The only barrier to entry is a good search engine that turns out results people want. It's not that hard, but it's far to easy to want to screw up those results to boost revenue, something yahoo was notorious for. Microsoft's biggest expenses related to search were advertising (such as buying Yahoo's search business) and trying to convince people they could be trusted, so far they've mostly failed at both. Even at that Bing is still not as good at returning results as Google is. Maybe that's because Google's entire company is devoted to search and Yahoo and Microsoft are devoted to other things with search being a second class citizen in the company.
But actually a good thing. Of course you'll deny that if you drank too much of the neo-conservative cool-aid, but to any thinking person it's quite clear that the total dominance of a few global superplayers is not beneficial to the market or the people.
You might like putting people in jars but I don't, please don't attempt to classify my political leanings by putting me in a jar, particularly one I despise. The problem with your argument is that the total dominance of Google as you claim could be replaced overnight by people typing a different URL in the bar. There is no barrier to entry other than excellence in search. What I see in search is a very functional and competitive market place. Google messes up once and the lions at their door will eat their market-share in a matter of months. The total lack of barrier's to entry, the ease with which consumers can switch and the fact that prices are falling indicates a healthy free-market, even if one of the players is dominant. All regulations will do in a situation like this is break the functioning market. I'm all for regulating markets, just not doing it to ones that are functioning relatively freely.
European regulations should be focusing on the edges of the market where Google is trying to manipulate things, such as forcing them to randomize product listing instead of always listing their own first. Or making sure they don't turn their Android system into a vehicle to mobile control (but by all reports Europe has a healthier mobile competition than the US with a functional player in Microsoft). Or even leveraging their android wear or android car to gain control of other markets. Again though the touch should be light, by all accounts these markets are free and functional. Overly heavy regulation is as damaging as no regulation at all.