It is nice to be responsible for respected things. As a rule everybody will like to be named as an author in a "paper".
On the other hand it is not so nice to be responsible for things which may become displeasing. Therefore the responsibility for work safety has to be directed. As a rule the responsibility is top-down delegated. The top level is the president of the university. The delegation stops at the professors in the instituts. Every sub-delegation will be more and more detailed.
It is OK if the professor delegates special jobs to co-workers, but he will be still responsible for the organisation, for the selection of suitable co-workers and for checking if the delegated jobs are done properly.
A transfer of responsibility has to be done in written form and has to be confirmed by signature.
It is true: As long as nothing happens usually nobody cares if this is handled properly. But if an accident has happened and there are legal investigations about culpability and liability, prosecutor and judge will insist to see documents proving a proper safety organisation. If there are no documents showing that the responsibility has been transferred it must be assumed that the transfer has not happened correctly. In case of a lab course there is a very simple evidence: Responsible are the lecturers listed in the offical course book for the lab course.
Note: Responsibilty is always strictly connected to the decision-making authority. Staff who is not allowed to make decisions cannot have the responsibility for given decisions and has only to report to the boss if there are safety problems.