Here's an analysis of three civics: Merchant Trade, Regulated Trade and Free Enterprise. They multiply your commerce in different ways: MT +1 trade route in every city; RT +50% commerce in capital city; FE +50% trade commerce in every city (secondary effects like +1 plantation commerce and civic upkeep differences are ignored for simplicity). Which one is the best? Here are two principles:
Principle 1: Free Enterprise is better than Merchant Trade, if and only if your city has more than 2 trade routes on average.
Proof: Take an assumption that there are N homogeneous cities. Each city's trade income is denoted by t*y (t = num of trade routes; y = commerce of each trade route); other income is denoted by z. This yields your total commerce Y = N*(ty+z), the benefit of Merchant Trade Y(MT) = Ny; the benefit of Regulated Trade Y(RT) = 0.5*(ty+z), and the benefit of Free Enterprise Y(FE) = 0.5Nty. Thus, Y(FE) > Y(MT) if and only if t＞2.
Since 2 trade routes is very easy to reach (lighthouse +1, post office +1, geography +1), it implicates that FE is almost always better than MT.
Principle 2: Free Enterprise is better than Regulated Trade, if and only if your total trade commerce is larger than your capital's total commerce.
Proof: Since Y(RT) = 0.5*(ty+z), Y(FE) = 0.5Nty, Y(FE) > Y(RT) if and only if Nty＞ty+z. The LHS represents your total trade commerce, while the RHS represents your capital's total commerce, including trade commerce, tile commerce, specialist commerce, etc. Both are available in your game.
This implicates the intuition that RT is better with a strong, or potentially strong capital, while FE is better with a large-expanded empire whose capital is not that important. Since trade income could be multiplied a lot in late game, and you may want to expand your empire and get more and more cities in late game, it is suggested to switch from RT to FE in a certain time, which is accurately given by the principle 2.