Is there any advantage to not having a build que free with nothing being built
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Yes. If you are building no social improvements then you are not increasing the financial burden of maintenance costs on your empire. Different players prefer different approaches but when money is tight, we all agree that the zero maintenance social builds are most attractive while the social builds with high maintenance costs require careful selection. For example, high planet quality (PQ) planets may need little or no morale boosts but low PQ planets may need several morale boosters (entertainment, stadium, teleporter, harmony generators, etc.). Or, if you are only buiding your big warships on your best planets, then don't waste money to build ship quality boosters on planets where you don't build ships.
Aldar's comments about the constructor were *very* true with version 1.05 and prior versions where constructors were zero maint. Now on 1.1, constuctors cost 1 bc per turn to maintain so I quit building constructors too after I have built an adequate number and pretty much have the game in the bag. At the end of the game when you are taking over the opponent's star systems you will probably lose some trade income so why build (and pay for) anything you don't need?
Freighters are still zero maint so they are always fine to build and park next to potential trading partners and as Aldar says, you can always gift them. They also have good range to explore but are slow. The bottom line is to watch out for the cumulative effects of maintenance costs, especially at higher difficulty levels.
Oh yes. Many of us think it is a good idea to destroy un-necessary social builds on recently captured planets. The AI often builds everything and you can save dozens of bc per turn by destroying things you don't need on your recently acquired star system.
Hope this helps.