Your small vessels are not grown to tolerate a constant pressure. You get aneurysms, clotting is super dangerous because they generally form and sit rather than getting sucked/pushed into the heart to potentially get broken up. Most importantly, forget your potential organ failure you wont notice until there's a lot of damage, and all the numbness you'll get, it's the brain function affects that bother me. Sluggish, memory problems, et al that accompanies tiny thromboses.

A rotary pump is an endgame-solution. It keeps you alive, at a cost and you die the end anyway (obviously).

I remember reading, years ago, about someone who was temporarily fitted with a rotary pump. He said his hearing required some adjustment, apparently we sort of constantly hear blood rushing without being aware of it, but that somehow changes when your pulse is gone.

How do these pumps affect blood pressure? Does it become constant? That can't be good for the elasticity of arteries & veins?

I guess if we find that a pulse is required it will be relatively easy to add a "pressure relieve" valve to the rotary design. Pressure builds up and gets released regularly, just like ye good 'ol pump.

Pulse is central to traditional Indian medicine (Ayurveda) [1]. Will be interesting to see what the science finds, although I wouldn’t personally volunteer to have a pumpless-heart. Sounds likely to have unintended consequences as you suggest.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4890095/