Interesting. I tried a different approach: no limits, except for normal daytime activities (e.g. normal sleep time). The result was what I wished for: eventually things stabilized. Yes, we went through several 2-3 day binges, when our kid would be completely immersed, but eventually she always got bored and seeked other activities (especially social & involving movement). After those extended screentime periods, devices would always get cast aside and used sparingly. So, it seems that at least some kids at some ages are able to maintain a reasonable balance all by themselves.

I don't know if this can hold (she's almost 6 now), but so far I'm very happy with the results.