You should search for w2aew's videos on op amps. Also, Dave has done some.
If you use 2 supplies to create a + and - voltage, you have 4 wires, Where are you going to put them? It's obvious what you do with the intended + output and the intended - output but what about the other 2. That's where you tie them together and also create the circuit ground. All signals will be + or - relative to ground which we will call 0V.
You can most definitely use a dual supply op amp on just one supply. BUT, you have to have your AC signals revolve around Vcc / 2. There are chips called 'rail splitters' that create this voltage or you can do it with resistors and probably an op amp as a voltage follower to lower the impedance. This is done all the time but the Vcc / 2 thing is a PITA. It just gets in the way if you want your input and output signals to revolve around 0V. Yes, blocking capacitors help but it's pretty easy to get dual supply voltages so why bother?
While I'm on the subject: "Op Amps For Everyone" is a great, and free, reference and they spend a lot of time talking about single supply op amps. Google for it...
Despite what I think about Vcc / 2, single supply op amps are the most commonly used at this point. In production, nobody wants to create two voltages when they can design around it.
I can't get around it because my only application for op amps is analog computing and some functions just naturally go below 0 and it would be truly ugly math to offset all the signals by Vcc / 2. It could be done but it isn't conventional and it wouldn't match what is covered in the text books.