They do, they really do. The problem is, defense attorneys tell themselves that there is both a constitutional and a judicial preference for warrants and therefore the already difficult hurdle of demonstrating an unlawful search is nearly insurmountable.
But the vast majority of search warrant affidavits have flaws, significant flaws that are often impossible to fix, since - depending on the flaw - the officer wouldn't be allowed to testify to back-fill the holes in his affidavit. As in all suppression cases, recognizing those flaws is the hard part. But just as police officers tend to rely on boilerplate for their affidavits, and thereby repeat the same mistakes over and over, the more search warrants a defense lawyer sees, the easier it becomes to identify the errors. (See, for example, this common flaw in search warrants, which - once you know it's out there - is easy to identify.)
This week, oral argument at the United States Supreme Court involved a long discussion regarding not just whether a particular search warrant affidavit lacked probable cause but whether it was so lacking in probable cause that the officers were incompetent for executing it, despite a magistrate's approval. A summary of oral argument is here. It is worth reading, because many of the questions that the justices asked the lawyers were the types of questions a defense lawyer should be asking himself about probable cause, when reading a search warrant affidavit.
I've certainly seen search warrants in Oregon based on less than the one under discussion, even though, again, the issue wasn't so much whether PC was missing but whether it was obviously missing. But the failure of defense lawyers to challenge these search warrants has resulted in the scope of warrants expanding over time like The Blob, broader and broader warrants that look increasingly like the general warrants that the 4th Amendment - in particular - was designed to eliminate.