GPS altitude is considerably poorer than GPS lat/lon. There's a good chance that your GPS altitude could be 10-20 metres off what it should be, which is enough

GPS altitude is considerably poorer than GPS lat/lon. There's a good chance that your GPS altitude could be 10-20 metres off what it should be, which is enough to be dangerous if you're using it as a landing aid. "True" altitude requires you to both have an excellent fix on the satellites and have a very, very good reference geodetic model (which you probably don't). Also depending on the quality of your fix, you'll have different altitudes to the rest of the people around you. It makes more sense to have two pilots independently check the pressure settings (and that's why you have a checklist).