Due to the natural dissipation of alcohol and other intoxicants in a person's blood, time of search is an issue in DWI cases.
Law enforcement needs:
(1) consent, or
(2) a search warrant based on probable cause, stated in the PC affidavit, or
(3) proof of exigent circumstances that excuse the failure to get a warrant (a tough showing for the state).
If you have an accident, the state can take your blood? Is that what you are saying?
You misunderstand the law, and/or appear to not believe in the constitution.
1. A wreck, no matter how egregious, is not PC for a blood search warrant.
2. There are no "silly delays from your lawyer" when it comes to blood testing in DWI cases. Lawyers are not involved, there is no right to immediate counsel on the side of the road. Lawyers get involved well after the incident, particularly when cops do not perform their duties correctly.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
It's really not that hard for law enforcement to follow the law.