The Imperial College report[1] found suppression to be effective even with much less compliance. Here are the different measures they modeled and the assumed compliance, taken from the table on page 6 of the report and edited out the info about assumed impact on transmission, for brevity.

> Case isolation in the home — Assume 70% compliance — Symptomatic cases stay at home for 7 days. Household contacts remain unchanged.

> Voluntary home quarantine — Assume 50% compliance — Following identification of a symptomaticcase in the household, all household members remain at home for 14 days.

> Social distancing of those over 70 years of age — Assume 75% compliance

> Social distancing of entire population — Assume 75% reduced contact outside household, school or workplace (the wording here is different, does not mention "compliance")

> Closure of schools and universities — 100% of schools, 75% of universities

I would recommend reading the report. Unlike certain summaries, the report itself is very clear about all the assumptions baked in, and so you won't get a false sense of "This is 100% how it will be". (That said, I'm not questioning their numbers since I think they're likely more accurate than any I could come up with myself).

[1]: https://www.imperial.ac.uk/media/imperial-college/medicine/s...