As billbrochin mentioned above, FDA definitely does require it. CFR - Code of Federal Regulations Title 21 117.335 requires documents to include date and signature. I have attached the whole regulation below for your reference. In this case it is good to have the signatures.
[Code of Federal Regulations] [Title 21, Volume 2] [Revised as of April 1, 2020] [CITE: 21CFR117.335]
TITLE 21--FOOD AND DRUGS CHAPTER I--FOOD AND DRUG ADMINISTRATION
DEPARTMENT OF HEALTH AND HUMAN SERVICES SUBCHAPTER B - FOOD FOR HUMAN CONSUMPTION
PART 117 -- CURRENT GOOD MANUFACTURING PRACTICE, HAZARD ANALYSIS, AND RISK-BASED PREVENTIVE CONTROLS FOR HUMAN FOOD
Subpart F - Requirements Applying to Records That Must Be Established and Maintained
Sec. 117.335 Special requirements applicable to a written assurance.
(a) Any written assurance required by this part must contain the following elements:
(1) Effective date;
(2) Printed names and signatures of authorized officials;
(3) The applicable assurance under:
(i) Section 117.136(a)(2);
(ii) Section 117.136(a)(3);
(iii) Section 117.136(a)(4);
(iv) Section 117.430©(2);
(v) Section 117.430(d)(2); or
(vi) Section 117.430(e)(2);
(b) A written assurance required under § 117.136(a)(2), (3), or (4) must include:
(1) Acknowledgement that the facility that provides the written assurance assumes legal responsibility to act consistently with the assurance and document its actions taken to satisfy the written assurance; and
(2) Provision that if the assurance is terminated in writing by either entity, responsibility for compliance with the applicable provisions of this part reverts to the manufacturer/processor as of the date of termination.