Your normal altimeter fitted to most training aircraft isn't a sensitive one. These are the same as most standby altimeters. Which is why its not abnormal to have anything up to 500ft split in them depending how fast you are climbing. They will sort themsleves out with a wee bit of a split in cruise. They don't use sensitive ones on the standbys because they are more expensive and require a power supply.
The encoder bit is just an add on to the sensitive altimeter.
There used to be tons of errors and encoder issues (not with standing human error with setting the thing) which is why most transponders now have there own built in pressure sensor.
As I qualified I am a meer driver with a theory not a avionics engineer