Correct me if I'm wrong, but that's because SD cards are half duplex, right? So there's no way to disable writing through a "disconnect pins x and y" because those pins are needed for reading.
SPI is full duplex; it has a dedicated line per data direction (MISO and MOSI), however the same lines are used for commands and data. So with MOSI (master out, slave in) physically disconnected, it'd be impossible to send the command asking to read data, even though that data would be delivered on the separate MISO (master in, slave out) line.