Customs and Border Protection is mostly a continuation of the US Customs Service, which had existed since the beginning of the American state, but was combined with Immigration and Naturalization services as part of Bush II's executive overhaul that made the DHS. ICE was an entirely new agency under DHS. There have always been customs agents at ports and border stations, but agents that patrol the homeland looking for people without a valid visa is something that came about more recently.

If you were to take customs agents out of airports, this would open them up to all kinds of "unrecorded duty-free imports". And once they make it into America they could go anywhere in the country. This retaliation probably won't happen because it would be a spectacular self-own.