In addition to slowness, the Linux drivers for SD cards are notoriously buggy and produce data corruption from time to time. This affects even laptops with “eMMC” SSDs (essentially, a high-speed SD card soldered onto the motherboard).

Can you install Linux on SD card?

Installing Linux on an SD card can be done. A good example is the Raspberry Pi, whose OS is always installed on an SD card. At least for those uses, the speed seems to be sufficient. If your system can boot from external media (e.g. USB ssd drive) it can be done.

Can you run an OS off an SD card?

Yes. Actually, it seems snappier than the spinner in the laptop. The SD card is a UHS-1 card rated at about 45MB/s. Faster seek times probably makes it feel faster than the hard drive.