You cannot ignore cases, ICU admissions and deaths are lagging indicators and are affected by the age profile of the numbers.
Every indicator shows case numbers are rising arguing whether it is a wave or not is simply arguing over a definition that you can choose to define how you want.
There are quite legitimate debates to be had about how much death is reasonable to accept, how much restriction is reasonable for society etc.
But arguing that cases that haven't so far resulted in death or disability don't represent a real rise in transmission or is somehow not a wave is meaningless.