The "trustee" has legal responsibilities, and the "named fiduciary" must be identified to the IRS & Department of Labor to provide compliance information.
In a small business the "sponsor" almost always uses a third party as a "plan administrator" but the owner or other highly trusted employee has the legal responsibilities of "trustee" and "named fiduciary". There is no legal reason NOT to do this and there is only extra cost with hiring outsiders for these roles.
Anyone in the the firm that has demonstrated an ability to maintain timely and accurate information about employees, is privy to compensation information, and has an excellent sense of confidentiality is suited to the roles, and anyone who has NOT demonstrated those qualities should be eliminated from consideration.
Answers to 401k Trustees & 401k Fiduciaries Responsibilities