I'd call it YMMV.
I've spent a lot on dental bills over the years. A LOT. I also get to spend more now, because apparently a prior dentist did bad work on my mouth that needs to be redone. (There is a persistent red infection under a crown put in 3 years ago for example, which I'm told shouldn't happen.) This year it's $1300 (pre-tax) and next year I've got another $1300 in work planned.
So, for me, an electric toothbrush saves me money. Could I brush and set a timer to brush for two minutes? Yes, absolutely, so this can be seen as unneccessary. Did I, in 32 years? No. Only 2 years ago when I got the electric and got tired of high dental bills and got a dentist that scared me into flossing every day, brushing two minutes, etc, did anything change. So for me, I save money overall this way and get better cleaning for really bad teeth than I would if I used a manual and set an alarm.
But I do hate the high replacement head price, so I use them much longer than I should and I try to coupon to better prices.