You can frequently avoid this by running at a lower voltage - SPI chips are often rated to run down to under 3V, and associated components will tend not to run with that much power
I tried to use something like this to read a flash on a car’s ECU. I even build a small probe station when the clip finally broke. I ended up having to desolder it. I don’t understand how hackers make in-circuit spi probing work on embedded systems. It always just magically works for them to clip a Pomona on and go. I don’t get it.
Powering the chip will inevitable power other things around the chip, things that might also be trying to read it.