If I remember correctly the problem was the new models were imitating (with software) the old ones to avoid having to be certified again.

When it was time to fly there were slight differences and this caused the pilots to react in the wrong way for the new model's behaviour.

While I understand the reasons you mention, I do not clearly follow the distinction between cutting on costs and cutting on quality. It seems like two sides of the same coin.

This is getting finnicky, but generally I would consider a quality issue to be something to do with the build (ie substandard materials, poor riveting, trash in the dead spaces in the walls - as has been alleged on the 787) as opposed to what happened, (in my view) which was cost cutting - as you point out, they basically tried to do a software emulation of the previous 737. The issue isn't flight worthiness - the 737 MAX can be a safe plane - but they cut costs by not wanting to do a recertification or retraining. I guess that is a quality and safety issue, but not what i'd normally consider quality?