Not only would I not close without a title search, I wouldn't even take a gift of property from my sainted aunt without owner's title insurance to back up that title search.
JK is 100% right here in what could go wrong. Further eschewing a proper closing, can result in you getting left on the hook for things the other property should rightfully be paying for (prorated taxes, utilities or other assessments, etc...).
Further using a self-written deed may not convey what you think it does (even beyond JK's points about the seller not having the interest he claims he is conveying). Even the property I sold to one of my tenants which we did without real estate agents, etc... I paid my attorney to handle the actual closing and filing the deeds, etc...

