Then you're just going to have to plow that revenue back into happiness building maintenance.
Think about the game mechanics a little differently. You're not founding new cities to get money, even as Arabia. When you use a Settler, you're effectively putting a permanent improvement on the tile. A 2/2/1 tile is much better than the tile was before it was settled. You also add up to seven tiles to your territory immediately, and make a few citizens arrive faster. The cost of doing this is happiness, hammers (and food) invested to build the Settler, and having a hammer stream that is distinct from the one that spawned the Settler.
Your bonus to trade routes effectively enables you to grow horizontally to spots without luxuries and still finance expensive Colosseums and Circuses in response to the Happiness problem. There can be reasons to want to do this. Luxuries may be scarce or distributed in a small number of desirable spots that must be settled early. Defensible positions may not be conveniently located next to the luxuries. Prospective barracks city sites that lack luxuries may just be too good.
Your trade route bonus will permit you to afford to be a little more spread out than other players. That means better tiles, which likely means more hammers in the long run (either through better tiles worked or fewer of your units dying). Just don't take it to extremes.
Another way to think about it is this: there's a growth curve in this game. As cities get large, they grow slowly. If you want to maximize science, you're better off plowing food in a large city into creating a new production site that grows rapidly, rather than having it rot while you wait ages for a new citizen. The only exception is large cities where you have stacked a ton of science improvements already.
The trade route bonus lets you start on that process a little sooner than everyone else, because you can afford to pay for happiness building maintenance. That translates into larger populations and more science. So you could look at your passive trade route bonus as something that is convertible (at the cost of some hammers) into a passive science bonus in disguise.
Either way, don't try to found cities to get income as Arabia. It won't work. You found cities to get other things; the passive trade bonus just helps you keep the books balanced when you do.