This seems a strange idea, as it is the PI who takes ultimate responsibility for the study site and all delegation of tasks, not his/her sub-investigators. In ICH GCP 4.1.5 the PI maintains a list of suitable qualified persons to whom the investigator (PI) has delegated significant trail related duties. That is, the PI must either perform all the duties himself or he must delegate some of those task (but not responsibility for oversight) to suitability qualified and trained individuals. The FDA have a more demanding requirement that each investigator signs their FDA 1572 form, "statement of investigator". This form is signed by the PI to state that:- "I agree to conduct the study(ies) in accordance with the relevant, current protocol(s) .... I agree to personally conduct or supervise the described investigation(s). Also the FDA new guidance on investigator oversight of their investigator centre (Guidance for Industry Investigator Responsibilities, Protecting the Rights, Safety, and Welfare of Study Subjects, Oct 2009), gives a lot more information on what the FDA expects in its ten point plan:- "The investigator should develop a plan for the supervision and oversight of the clinical trial at the site. Supervision and oversight should be provided even for individuals who are highly qualified and experienced."
There are many Warning Letters from the FDA to PIs who fail to personally perform or personally supervise those they have delegated trial related tasks to. I am sure that the EMA inspector do the same (although their inspection reports are not made public)

The MHRA GCP Guide makes it clear that they anticipate that only the PI will delegate duties to their staff (11.3.4) :- "In order to demonstrate that the PI has authorised appropriately trained and qualified individuals to undertake certain trial related tasks, a delegation of authority log is used at the site. This document may be combined with the site staff signature log, but should clearly state the name of the person, their role and the activities they are delegated by the PI as well as being signed and dated by the PI prior to the activity being undertaken by the individual. It is not acceptable for the PI to simply sign-off the delegation log at the end of the trial. The delegation is not just a paper exercise; it is documented evidence of appropriate delegation of investigator’s responsibilities".

RQA (formally BARQA) answered a similar question on their GCP website (www.theRQA.com), about the PI delegating their duty of signing the protocol or alternative contract, to show their agreement. You may find that useful.