"have consequences on" is correct and usable in written English. You can use it to describe how something has an effect on another thing. For example, "The frequent droughts have consequences on the local wildlife.".
Experiencing pain at newborn age may have consequences on one's somatosensory perception later in life.
The three components of population change (i.e., fertility, mortality and migration) have consequences on one another and the overall size and/or structure.
Nations, like people, are bound to each other on this Earth, and the actions of one have consequences on the well-being of others.
On the one hand, it can have consequences on monetary aspects; on the other hand, it can have a focus on physical injuries.
Consequently, the way clinical teaching is carried out will have consequences on students' abilities to learn and understand.
So whatever budget deals are struck now — or avoided — will quite likely have consequences on the next mayor's decision-making.
No other show is so adept at marrying the epic to the personal, showing you how the smallest of actions can have consequences on the grandest of scales.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu