Avira,
Ki gerim heyisem is similar to ki bichipazon yatzasa
They are taamei hamitzvos. That doesn’t necessarily mean they are the actual reasons. We don’t really eat matza just because we left in a hurry. That’s what we tell a 5 year old, but there is a whole lot more.
But let me know if you do eat matza only for this reason or if you do love gerim only because you too were a ger in mitzrayim.