Does ECO mode hurt the engine in the long run?

Go back and put the display I suggested in Post#20 - it'll show that the ICE isn't flogging itself alone - MG2 will be assisting it.

If you're really worried - which I wouldn't bother - before putting it in gear, give the accelerator a stab - and it'll start the ICE and waste some fuel warming it up.

 

OK.....well......the only way to keep an engine from wearing is:
Dont use it. EVER.

 

Using a block heaters helps, giving the engine a leg-up on the warm-up process. A stone-cold engine with oil drained down is the toughest time for engine wear.

 

I'm not aware of any modern car that recommends warming it up before driving.

 

I arrived at $work one morning when there was some kind of freakishly popular event on, and zero vacancy in the parking garage, and I went up and down the whole thing two or three times before finally spotting someone returning to a car and getting in, and the brake lights flickered, and I stopped and waited, and about five more desperate drivers piled up behind me, as we all waited ... for the driver ... to warm ... up ... her Prius.