Single-lever shower faucet - no warm water; just hot/cold
Yes a bad cartridge can be the issue.

I speak from experience, you may want to forgo buying said cartridge until you take it apart and inspect the valve and parts.

Often times pieces of plastic, rock, minerals, bad sweat 'balls' and other contaminants can get in there and bind the mixing valve in the cartridge.

Also, if you find it is cracked, warped, or otherwise damaged, you might want to get the replacement from a reputable parts supplier. I was stunned to see that Home Depot was selling all plastic and Kohler OEM part was 90% metal (OEM, pronounced as separate letters, is short for "original equipment manufacturer").

I tried the Home Depot part to no avail. The OEM part worked and continued working at least for 8 years until I sold the place.