Get a decent quality keyless chuck and you will never regret it! I use one on my mill (1 1/2 hp BP clone) and I have drilled holes up to an inch and a quarter with no slippage unless I got aggressive on the feed.
You're very right allenr, larger sized drills certainly should have a hex shank, especially ones over 1/2. I have milled 3 flats on some shanks on larger drills for myself and for a friend, easy to do if you have a mill and semi universal dividing head! Sure makes a huge difference in the holding power a chuck has to develope to prevent slippage!
Tangs, or "drive key" as you call it, on Morse tapers are not there for "holding power". The taper itself, combined with an axial load, is what generates the holding power. IF the tang on the drill bit can engage the bottom of the socket on a DP, it definitely adds to the holding power, but it isn't the main force by a long shot. (Try milling with a MT endmill and the radial load will walk the taper out under all but the lightest loads. MT endmills need to be restrained with a drawbar.) On another forum quite awhile ago they did the math which proved the tang did not have the physical strength to prevent the taper from spinning. It's soft, and has little area, just the shoulders of the tang, bearing on the spindle and would twist off under a heavy load. They are there to give a wedge shaped drift something to work on when you want to remove them from a female M.T. socket (when they cannot be tapped out from the end) without damaging the end of the taper...damage which could very well prevent it from seating properly into the socket the next time it was used. A wedge shaped drift is placed through the tang slot in the DP spindle and quill between the end of the tang and rear end of the slot, and struck with a hammer which forces the MT out. On lathes, you can reach in through the spindle to tap the MT out of the headstock end and on the tailstock end, cranking the barrel all the in back brings the MT into contact with the end of the screw and forces it out that way.
That is the most wrong statement I have ever heard concerning a lathe. YOU DO NOT WANT A MT TO SPIN IN EITHER THE HEADSTOCK OR THE TAILSTOCK!!! Spinnning in a socket, (just once is enough!) can damage it by raising burrs, especially if it is not a hardened socket. A soft socket can be repaired by judicious use of the appropriate sized MT reamer...repairing a hardened sockets is another story,but it can be done. Cleanliness of both the male taper and the female socket is also of utmost importance before seating the drill into the socket. Wiping both with a lint free cloth to remove any coating of oil isn't over kill. A VERY TINY bit of foreign material in the female socket is enough to cause problems. Dings in the male taper can raise metal and you should check for that and use a slipstone to remove it. The fit between the male and female parts should be as perfect as you can get it. If it isn't, the taper does not seat properly and if it doesn't seated properly, it doesn't develop it's full holding power and the probability of slipping is very high, which means it will probably raise burs and the whole Catch22 situation continues.
A little error in wording, MT are not held in a chuck on a lathe, they usually either go directly into the spindle which would be a female MT socket or you use a MT adapter, usually to size down a size. E.g. from #3 MT to #2 MT. Usually a MT drill bit would be held in the tailstock, which is often one size down from the headstock size.
The fact that you can use a MT in a lathe which has no provision to drive the tang pretty well also negates the idea that the tang is a driving device. However, it is also prudent to use a lathe dog to give backup holding power to the bit if you are doing a heavy cut. It's easy to do on the tailstock side and with a faceplate on the spindle, also easy, and an ounce of prevention is definitely worth more than a pound of cure in this case.