Here is a list of kites which are 4 line kites with single center flagging that come with a control bar that uses single center flagging which you can use for kiteboarding (not a complete list):
Envy, Wow, Solo, Elite, RPM, Turbine, Wave, Rally, SST, Pivot, Slash, Dash, Ride, Boxer, Fy, TS, Roca, Switchblade, FX, Drifter, Apollo, Contra, Radar, Union, Catalyst, Enduro, Reo, C4, Edge, Zephyr, Evo, Neo, Dice, Rebel (as of this year), Mono, Juice, Rabbit, Maniac, Nitro, Element, Helium.
Here is a list of C kites. They often use the Y lines as you mentioned sometimes with 4 lines, but are not for beginners. All of them have the capability of riding with the 5th line both for safety and relaunch.
Legacy, Fuel, Torch, GP, Vegas.
The kite you imagine, the one with the two center lines that joins into a V, has a bridle, releases to the 2 center lines, that system is called a "mini 5th" and is extinct. Ocean Rodeo has an option to ride one of their kites in the mini-5th configuration that's it.
Modern kites have something called: Single Center line flagging. You ride that. Or you ride a C kite. I have no idea where you are getting your information from. It is quite old.
Trainers don't require safety systems (you can just release the bar) and can run on 2, 3 or 4 lines, and their control system, and bridle generally don't have much to do with the power kites we use every day. They are excellent for learning but don't require the more sophisticated safety system of a power kite.
If you are looking at power foil kites, the only use for the 5th line is for the safety. If you throw the QR on a foil kite and have the flag out line attached to the single center line it twists everything into spaghetti, which is why most modern foil kites use a 5th line, but relaunch using system peculiar to foils (such as reverse relaunch).