Yup, any oil's better than *no* oil, agreed!
But... One of the additives in motor oil is a detergent, designed to keep the crap suspended because *it all gets filtered* in a vehicle motor - most lathes aren't fitted with a filter, so the crap gets repeatedly passed through the bearings, between the gear teeth etc. - machine oils don't have the detergents, so the crap will at least settle in nooks and crannies, getting it out of circulation (eventually).
A lot of the extreme pressure (EP) additives in modern motor oils / transmission oils can also be quite hard on copper / zinc alloys (e.g. bronze / Oilite bushes, thrust washers etc.), so aren't a good idea

OK, the machine makers don't have their own refineries, but the guys who do (Shell, Castrol, Mobil etc.) make oils specifically for machine use - and the lathe/mill/whatever makers pick one or more that match the working conditions they expect - most often a standard hydraulic oil, sometimes something a bit more exotic - like mine, the original recommendation for the headstock was Shell Tellus 2, now discontinued, an ISO 5 hydraulic oil, which is incredibly thin (high-speed plain white-metal bearings are fussy!), the current replacement is 50/50 LHM hydraulic fluid (used in old Citroens and Rolls-Royces for the suspension, steering and brakes) and paraffin to get the right ISO viscosity...
Running too heavy an oil in plain bearings will probably reduce the flow and so the lubrication, too light and there won't be the hydrostatic "cushion", so increased risk of contact and wear, too heavy an oil (or too much!) in a roller bearing and it can cause "hydraulic locking" where the rollers stop rolling and skid on the races, with increased wear or even seizure... Not nice!
Dave H. (the other one)