I'd be happy to make this available as an option, but there are some technical issues with implementing it at the moment. Hopefully it'll be reasonable to implement in the future when the UI code gets a refresh.
I'm not sure if you like a blinking caret because it's soothing or because it's easier to find again after you look away. If it's the latter: I tend to lose track of a caret even when it's blinking, and I just alternate pressing the left and right arrow keys until I see it again.