If you're looking to make a point on constitutional grounds, I would contend that the real problem here isn't that Gates was arrested, but there is even such a thing as a "law enforcement officer" whose mere existence is an abrogation of the responsibilities of free citizens.
It's no coincidence that there are parts of this country with almost no law-enforcement presence at all -- and they have no crimes, either.
With no law enforcement officer, you effectively dismiss all laws.
With no ability to enforce laws, there’s really very little need for courts.
With very little need for criminal courts, there’s very little need for jails or prisons.
It seems you have found a solution to the problem of crime.
I’m sure the crime statistics would drop precipitously.
God help the public citizen, because nobody else would be around to.