It doesn't make any sense for me, why would someone use those very hi fidelity op amps with nothing connected on input and output
These symbols represent the power supply pins for op amps that are used elsewhere in the circuit. Note the reference designators: U3C, U4C, U8C, and U14C; this means that they are the third sub-unit of each of U3, U4, U8, and U14. Furthermore, note that these sub-units don't have input or output pins. By putting these supply sections separately from the amplifiers themselves, it's possible to make the schematic neater by separating power and signal portions in the drawing (and showing power supply considerations like decoupling in context, as Transistor pointed out in a comment).
Since the NUM4580E and LM562 are dual op amps, for each of these symbols, you'll find schematic symbols showing how the two actual amplifier circuits (U3A, U3B, U4A, U4B, ...) of each dual op amp chip are connected to the signal. They will be elsewhere on the page, most likely in the signal chain, and won't include the power pins but will include the inputs and output. This separation also allows the two amplifiers on each chip to be located in separate locations on the page, if they logically don't make sense drawn right next to each other.
You may also find that in some cases, an op amp is connected "uselessly", e.g. with its inputs tied together or tied to ground. This happens if there are any unused op amps (e.g. seven op amps are needed and there are 8 available), to ensure that they're in a known good state and not floating/oscillating. Texas Instruments has a document about it.