Revisiting HotStuff with Kartk Nayak, we observe that two phases are enough after all to achieve all the desirable properties of HotStuff, namely: Optimal (quadratic) worst-case communication against a cascade of failures, optimistically linear communication, a two-phase commit regime within a view, and optimistic responsiveness.
See the HotStuff-2 writeup on eprint, https://eprint.iacr.org/2023/397.
Also, read our post What is the difference between PBFT, Tendermint, HotStuff, and HotStuff-2?, illustrating HotStuff-2 and explaining the differences from PBFT, Tendermint, and HotStuff.
