There's no TDA rule about the line for more reasons than you realize. Once you have such a rule, you'd also need rules about the design itself. Rules about the size and shape of the table and position of the line, etc. That's just way too much headache and beyond the scope of what the TDA should be governing.
Besides, as you pointed out, not all tables have them, including tables in the same room.
For what it's worth, the real purpose of the line has nothing to do with poker. It's so that when a maintenance person is changing the cloth, he can measure and make sure it's centered so that the other artwork is where it was intended to be. Probably more important in the pit where the cloths are way more artistic, but you get my point. Watch a guy changing it. He'll walk around that table, measuring and tugging, for a dozen laps before he's satisfied and starts to staple it in place.
Bottom line, leave it as a house rule.