It is important to understand the context and timing of the Imperial paper. It was produced as part of UK government decision making in the days leading up to the 12th of March in order to make a binary decision between to immediate alternatives: Mitigate and flatten the curve or suppress and crush the curve.
It was well understood by the authors that a permanent lockdown was not possible and that there would need to be a step 2. They did some modelling of possible step 2 (proposing alternating lockdowns with relaxations for example) but did not go into detail on other options such as enhanced contact tracing, widespread testing, or other options.