Suing the government is a long and expensive process. Most criminal defendants couldn’t afford to pay a lawyer to fight such a case. Few attorneys would be willing to take that kind of case on contingency except for the most obvious and egregious violations, so any remedy would be available only to the wealthiest defendants and in the most severe cases. The net result is that most people suffer a drastic reduction in their 4th Amendment rights.
Plus, any remedy available through that system would be incorrect. The only two relevant remedies would be some form of cash payment to the claimant and an injunction barring the government from using the illegally-obtained evidence against the claimant. In the case of the latter, the end result is a lengthy civil court battle against a much better funded and equipped foe (the government), which if successful only provides the result we already get automatically now. Either the criminal case has to be put off until the conclusion of the civil case, greatly lengthening the time between indictment and trial, or the criminal case would proceed before the civil case had concluded, thus potentially rendering the civil case moot because the claimant would have started or even finished his sentence before the civil court could rule on his claim.
Monetary relief is also an inappropriate remedy because it is not the best way to restore the person to his status before his rights were violated by the government. If the government bans a book I write because it finds the contents objectionable, I can sue and maybe win monetary damages - but I will also be allowed to distribute my book as I did before. If the government bans me from worshiping a certain god, and I sue, I may win money from it but I will also be allowed to worship the god of my choice as I was before. Similarly, if the government violates my right not to be subject to unreasonable search and seizure, or not to incriminate myself, I may win money, but the foremost result must be that I be returned to the same position as before my rights were violated - not subject to criminal punishments. I am not restored to that position if I suffer from the violation of my rights when that violation is known at the time the government imposes a punishment.
Monetary damages are appropriate when they are the only possible remedy. For example, if a person is convicted because a police officer illegally beat a confession out of him, and that illegal interrogation is only discovered after the person has served many years in prison, he must be compensated with money because it is impossible to turn back time and keep him out of prison in the first place. But if that illegal interrogation is discovered before the trial, it is not appropriate to let the confession be used to convict the person because he may have the opportunity for a different (monetary) remedy later. The better remedy is to prevent the confession from being used to incarcerate the defendant in the first place, and since that remedy is available in the second situation, it must be used.
Rights belong to the individual. Punishing the government for violating them is important, but the primary remedy is to restore the individual to his position before his rights were violated. As in my above examples, if the government were to violate one of your rights - say they prevented you from going to your church, or they took away a firearm you legally owned - would you be satisfied with a monetary reward after several years in civil litigation? Or would you insist that you be allowed to go to your church or have your gun?
Bravo. A VERY good post. Thanks!