Should Germany have kept its surface fleet active?

Would it have been better for Germany to keep the surface ships active because of the British resources needed to contain them?

Yes. Their continued activity tied down substantial British forces even when the German ships did not win a major engagement.

An active German surface fleet required British resources to contain it. Keeping those ships operational is therefore judged strategically preferable to abandoning their use. The gain lay in maintaining pressure on British force allocation even without an immediate battle.