A coordinated deploy that depends on one person staying late is a plan with a single point of failure, even when it works. I liked that your example was a small move, a site going from CRM hosting to IT, because the small ones are where nobody thinks a written plan is needed.
On the question in the replies about a minimum set for a small team, the list I would keep is short: a written statement of what deployed means for this change, one rollback step that has been tried at least once, a named owner for each team involved, and a check that runs after the release instead of someone clicking around. Anything beyond that can grow with the team.
A useful test for red tape versus a useful check is whether anyone can say which failure it prevents. If nobody can, people will route around it. Which check from that first deploy turned out to matter most?