Any moving or flexing part is subject to wear and tear, and the risk of eventual breakdown, necessitating replacement surgery every few years. Open heart surgery is involved, somewhat risky, and puts the organism under significant stress by its very nature.
To the best of my (layman's) knowledge, pulse is not really needed by the body, and using smooth flow pumps causes no health risk. Of course there's the inability to check for the pulse or its tempo, as well as the mental impact of not having the expected sign of being alive.
If this becomes successful, I can see doctors adjusting to other methods of measuring heart activity, but I don't see how they could be noninvasive.