[womberte]

What sort of 'auto' is it, conventional with a torque converter and epicyclic gears or an 'automatic' that is a 'manual' gearbox with one or two clutches which is electronically controlled?
As Fruity said, the additional shifts will increase the wear on the clutches and brakes in the transmission. I'd disagree about the backing off being bad, in principle, as the transmission will have a lot less torque to handle, reducing the high load slippage and wear, but that's just an opinion.
Personally, I hate transmissions which are 'over keen' to hold or drop a gear, regardless of it being potentially more efficient for economy, and will also ease off to encourage it to change up before gently applying a bit more throttle but short of causing it to drop back down again.
Most (all?) newer (last couple of decades) auto's use lock up torque converters which remove slippage as the 'normal' operating slippage is inefficient and hurts fuel economy.

I would remind you that, like all other parts of a vehicle, automatic transmissions also need regular checking and servicing, something that many people seem to ignore to their later regret - repairs can be damned expensive!