As I've understood it, the exclusionary rule is a prophylactic rule aimed to prevent the cultivation of illegal evidence collection by removing the utility of illegally-collected evidence through inadmissibility in court.
Another way to prevent illegal evidence collection would be through strong and fear-inducing punitive action.
The problem with the inadmissibility route (1) is that in certain cases, good evidence is thrown out. The limitations to the law that I've seen do not include any "if the evidence shows a grave crime, it must be admissible, despite illegal collection". It seems problematic that there can be blatant, undeniable evidence for heinous crimes, yet just because it was illegally attained, a blind eye must be turned and the criminal goes free.
One problem with the punitive route (2) is that it, to me, seems to go against the values of the US legal system. The way I see it, one can morally look at illegal actions done by a government official in two ways: (a) they are so important and have a hard job (esp. officers), so they should get more lenient punishments. (b) they are supposed to set an example and they have sworn an oath, when they break the law, it sends a message of hypocrisy and insecurity that breeds government hate and distrust.
Going with the (b) view, government officials should at least be given equally strong punishments, or stronger. It seems however, to my foreign and non-lawyer eyes, that the US is more in the (a) camp, meaning government officials should be given more lenient punishments. Given this assumption, route (2) would run contrary to at least one moral notion of the US legal system.
Another problem with route (2) is that it might wind up incarcerating or firing a lot of officers and agents, though some may say that is a good thing due to the nature of those officers and agents. The last problem that I can think of is that this system may be easy to exploit. If strong punitive action was taken against illegal evidence collection, yet it is still admissible, that leaves motivation to do it. So, officers may congregate and create a kind of group immunity to punitive action, with everyone swearing to each other to never testify against one another on matters of illegal evidence collection. This could then propel illegal evidence collection, due to there being no practical danger in doing it, since the majority of officers have each others backs. Investigaton would be done by officers or agents, and if they're in on it, then there's no chance. This would then propel illegal evidence collection, and it could maybe lead to graver violations of privacy during the collection, as the informal rules of "no testifying" would probably not include a bunch of clauses for when the privacy/legal violations were too serious to be allowed.
To me, the reasons I've given does make route (1) more favorable. However, I don't think I have figured out every reason that went behind the choice of (1) instead of (2). I am also not sure whether the reasons I've given are correct. One of my reasons was also based on an assumption that the US legal system holds the view contained in (b). So, what reasons did I get right/wrong, and what reasons did I miss?
After reading @Dale M's answer, I realize I forgot to specify I was talking about US jurisdiction, as I've only heard of this law in relation to the US. However, this led to a pretty good answer about whether or not countries in the West generally have an exclusionary rule or not. Interesting to see that, in the West at least, it seems to be pretty limited to the US.