As I've understood it, not having a pulse creates all kinds of problems, blood clots and whatnot. It's simply not good for the blood, nor the blood flow. The body isn't made for it.
Pulsatile flow doesn't have such issues, so a Swedish company called Real Heart is making a TAH that pulses like a heart.
So far they've done successful tests with sheep and tons of testing of various blood parameters which look way better than traditional continuous-flow TAHs. Clinical trials on humans should be coming up relatively soon.
I hope they make it, and can improve it and make it smaller to fit children etc. It's pretty interesting technology.