One problem is that using position to get altitude would require a detailed elevation map and that would use a lot of storage space or require internet.
But elevation maps are not detailed enough and position is not accurate enough to get accurate elevation. Think about standing on trail along steep slope. The position not being that accurate is fine since you know you are on trail. But altitude could vary wildly going up or down slope, or even up or down trail. It is probably similar to GPS vertical accuracy, but were going for more accuracy that barometer provides.
The maps are only used when resolving a 3 bird fix. As soon as you lock a fourth bird you can solve 3D directly rather than leveraging an onboard spheroid. Many receivers refer to a three bird fix as a 2D fix for that reason.
But elevation maps are not detailed enough and position is not accurate enough to get accurate elevation. Think about standing on trail along steep slope. The position not being that accurate is fine since you know you are on trail. But altitude could vary wildly going up or down slope, or even up or down trail. It is probably similar to GPS vertical accuracy, but were going for more accuracy that barometer provides.