Actually, not really. For one, no serious manufacturer currently even proposes a battery technology if it doesn't meet the most basic of the mentioned criteria.
Secondly, some of these, like storing at a low/high state of charge or high/low temperature performance are nowadays managed by the BMS - models that don't have that are already not competitive. The reason is that energy density already crossed the threshold at which some of the capacity can be spared for this purpose.
To me the more important question to ask than any of these is: is there a process in place to manufacture the batteries at scale?
That is what ultimately makes or breaks an emerging battery technology.