"with important consequences" is grammatically correct and can be used in written English.
It is often used to describe the outcome or result of a particular action or event. Example: The government's decision to raise taxes will have important consequences for the economy and the people living in this country.
But it's become a real issue with important consequences.
That is either a substantial power with important consequences or a trivial power with negligible consequences.
But people interpret these cues differently, with important consequences for their performance.
The September jobs report contains information with important consequences for government policy.
When it comes to resources and aid spending, money is valued differently by those who have had less of it, with important consequences for programming.
The question currently before the Staten Island court is a narrow one, with important consequences: Can the materials from the grand-jury proceeding be made public so that we can understand why, and how, grand jurors arrived at their decision?
To define certain words in such a way as to bring plants and animals beneath the same semantic umbrella — whether of intelligence or intention or learning — is a philosophical choice with important consequences for how we see ourselves in nature.
Much the same is true of other wealthy countries, in which life insurance has become a major channel of saving and investment, with important consequences for the national economy.
It also meant a considerable decrease in the proportion of Germans living within Habsburg lands, with important consequences in the rise of the national problem in the following century.
Other studies at the meeting confirmed that domestication lengthens development, with important consequences for behavior.
Agricultural landuse alters landscape pattern, with important consequences for native species.
