That's mostly just because the Big Three hold other people's money. All this really means is that it's more efficient for a couple organizations to manage or process all of the country's wealth/stock transactions than have tons of private individuals or small organizations do it. Of course that does make me wonder how they actually do the decision making, are the boards of directors just picked by BlackRock/Vanguard employees?
Large companies can only exist if they receive monopoly rents. Otherwise incumbents would be outcompeted by challengers and we'd see a convergence of many small firms with low profit margins. So yeah, its the responsibility of the government to regulate monopolization and they aren't doing it.
Yeah, it's a major consideration when determining if a merger should happen, e.g. Krogers. Just because its more efficient doesn't mean you get consumer benefit because you should expect them to profit maximize with monopoly rents. I mean definitely +1 on nationalize them rather than let capitalism go unfettered, but I'm making a general observation that large companies can only be large because they can extract monopoly rents, rather than just a barrier to entry to match efficiencies of scale thing.
The government fundamentally represents the interests of the class that holds power though, and under capitalism it's the people who own the monopolies.