If squatters should be rewarded with ownership for breaking laws, why don't we reward thieves by letting them?

Well the minimum time requirement for adverse possession (squatters rights) is 5 years and as long as 20 years and they must pay all property tax for the entire time to gain rights to a property, If there was and illegal alien living in the US and could prove that they paid all taxes they were required to then I wouldn't have a problem will allowing them squatters rights after a set time period like say 10 years. The requirements for adverse possession are very difficult to obtain and rightly so. When was the last time you heard someone who actually completed a take over of someones property.