In short, if illegal techniques can be used to find evidence, and that evidence can be admitted, that's a pretty powerful reason to use illegal techniques.
Barring that evidence is a way to prevent that abuse. Aggressively prosecuting the use of illegal techniques is another way, but given that we're not willing to prosecute prosecutors who railroad the innocent or government employees who torture other people, well, I'd say that's a non-starter.
When you take the stand in court you are an individual giving testimony though. The rule of law means that if you perjure yourself you should be tried.
/lives in Sweden, where all evidence is admissible, but where the prosecutors should, but don't, go after their own on transgressions.
I (and many others) view the government as a service by the people, for the people. It should adhere to the same laws and constraints that the people do in order to be kept in check and not all-powerful. One of these regulations is that citizens have powerful rights of ownership over their personal belongings and no one should be able to rifle through them without permission. Objects/data/articles/ideas can be held private for a multitude of reasons, and due process should be followed in order to gain access to these details. By removing the government's requirement to abide by this, you grant it an immense power to control and have knowledge of your life. That simply isn't necessary for the true function of government. Our original constitution and amendments attempted to protect its citizens from that fear.
There is no "they". There are individuals who influence each other, each of whom may change their position depending on the position of others. History is replete with the consequences of changes inspired by advisers to advisers of leadership.
There is no guarantee that you can influence outcomes, but it is exceedingly likely that if you believe that you cannot influence outcomes, then you will not.
If you're allowed to use evidence from an illegal search, there's a huge incentive to keep doing illegal searches.
If you want to curtail illegal searches, then you make such searches have a worse payoff.
Because to permit it effectively allows the end to justify the means. It would effectively permit law enforcement to ignore any and all laws they wanted to in the course of investigations in order to produce a favorable result. Why the hell would you only conduct searches within the bounds of the law if you could get the same result more expediently by just doing it however you want?
If the police are willing to break the law, then who is going to enforce the consequences for doing so?
General Warrants
More than 2 words - If one would give me six lines written by the hand of the most honest man, I would find something in them to have him hanged. - Cardinal Richelieu
You get into situation where you tell a prosecutor - find this guy guilty of something and throw him into jail.
EDIT: Not that it should not be prosecuted if something is found also, but WHY does the obtained evidence have to be dismissed?