I've been in a place of having dental insurance and paying out of pocket at various times. Since cleaning tend to be the main cost and tends to be well covered I find dental insurance to generally be a pretty good deal. I've generally stuck to the same dentist through changes in insurance and paying out of pocket and have never noticed a difference in the type of cleanings I got as a result. Hopefully you won't run into something like that.
Sometimes you have the opportunity of going out of network to a dentist of your choice and then making up the difference between what your insurance would pay an in-network dentist versus the dentist of your choice. Like I used to get tooth colored composite fillings in a time and place where amalgam fillings were still used. My insurance would only pay for an amalgam filling at the time so they paid that amount and I paid the difference for the composite filling.
My current dentist isn't in network to my current plan but it still covers her costs 100% for cleaning and x-rays, and my last cleaning was VERY thorough! It sounds like it may be worth trying out, crunching some numbers, and maybe even shopping around. Hope it works out for you!