Regardless of whether it is useful or not, I see a significant difference between the "classical" ICE (where trace is possible or available), and serially-communicating debugger with on-chip support (which is where the SiLabs etc. fall), where a possibility for trace is limited or nil (there are also other nuances in which these two solutions differ, all of them important maybe in 1.23765% of cases).

many "classical" ICEs (where you isert a plug instead of the uC chip) e.g. the low cost ($1k5) Ceibos do not have trace.

Thus as opposed to your "if no trace it is not an ICE" I go by "if it is running in real time on real hardware with the exact software to be released in the final product, without interfering with the operation (if not requested) it is an ICE" and then there are "ICE with trace", but that is an optional feature. Trace is not a requirement for a true ICE.

For "classical" ICE you can spend 1k5 and get one (e.g. Ceibo) or spend $10k and get one with trace (e.g. Nohau)

Erik