Total time on an engine is really only attached to the data tag. You can put together a brand new crankcase, new crankshaft, new camshaft kit and the old data tag, does the total time really mean anything on these little engines? Which parts are life limited by hours or calendar per a regulatory requirement? This really starts making sense if your plan is to immediately overhaul it, which is essentially going to include a conformity inspection and AD compliance check. When the engine is disassembled and components sent out to machining and inspection venders which components are sent out with a note of total time on them? These engines do not use life limit card tracking individual components from birth to scrap.
The only things that bother me about cores or any used engine for that matter, is not actually knowing it if its ever had a prop strike. I would never buy one that has had one. But every day engines are disassembled and inspected after a prop strike and returned to sevice and how many of those are breaking crankshafts? How many broken crankshafts are related to prop strikes? How many cores are accepted by the OEM with little to no records, PMA aftermarket cylinders, crankshafts, camshafts etc? Off track a bit but you get the idea