I take all the points mentioned, and suggest they apply to most 1930s aircraft. Just try driving a 1930s car or better still a vintage lorry in comparison to today's power-assisted, computerised featherbeds.
In fairness to my fabric-clad friend, remember she was designed for hard work, not for fun. The Tiger Moth soon teaches the importance of nose attitude and of energy conservation, and few of her trainees forgot their first half-turn of auto-rotation which so quickly developed into a spin. She was and is very difficult to fly well, but very tolerant when novices got it totally wrong.
Half a century ago I learned instrument flight basics by climbing into cloud in our once deserted airspace as even then the wartime IF hoods were long gone. If you can fly a TM on instruments you can fly anything and when I tackled my IR years later the limited panel was the easy bit!
Engineers loved the Tiger Moth, even though they were expected to have 40 or 50 ready for flight each morning. The Stampe is much lighter and more responsive, but it's fragile and I have known a few drop wings into the ground. The Chipmunk too is a pilot's delight, but I've seen that dainty rear fuselage wrinkled like a toothpaste tube after a heavy landing with drift. The Magister, I was told, was nice to fly but we wrote off several Miles machines due to glue failures. This was the fate of most of them.
The Tiger Moth on the other hand takes just about everything short of sticking the nose in the ground. Gravity fuel flow, so no pumps to worry about; the fuel tank sits in full view, easy to inspect. Only one pair of ailerons to maintain on the lower wing. Cables and pulleys in easy view. The simple undercarriage has a long stroke self-damped by brass colletts; grease it regularly and it lasts for years of intensive instruction. Hangar rash and minor vehicle bumps etc. need only a quick splice, a piece of fabric and a splash of dope. The wartime pupils broke most bits breakable, so DH came up with every conceivable repair scheme so the TM could continue doing its job day after day, year after year.
For all her failings, hopefully you'll agree that the Tiger Moth was unrivalled as the trainer of her time. Try one if you get the chance, I've yet to meet someone who has failed to learn something!