At first they did, then they realized how corrupt it made them look so they backed off and said they only objected to the procedures used.
The Judge issuing the warrant included plenty of safeguards for Congressional Privilege.
As far as being careful who has this power in the future, they will not be bothered by negative precedents, and the power is already there to be abused, and is already abused. Witness the trials of Tom Delay, et. al.
American Presidents are not Kings. They are selected, indirectly at least, by the people, the same as Congressmen. They have a lot more real checks on their power as well, compared to Congress as a whole.
The Constitution does not prohibit the executive branch from applying the criminal law to individual Congressmen. Any suggestion that it does is completely at variance with the text of the relevant Constitutional provision.
The real danger is when Congress, the Executive and the Judicial branches all decide that the Constitution doesn't mean what it says. Such as "Congress shall make no law... abridging the freedom of speech" and "the right of the people to keep and bear arms shall not be infringed". As in the case of CFR and the former "Assault Weapons Ban" (although the Supreme Court managed to dodge that particular bullet, by refusing to hear challenges to the law, even though they jumped right on CFR, upholding the vast majority of it, before anyone had violated it.)