This is one of those expressions that you should not try to translate from a language to another.
You are not actually asking about the time, but about the hour. That
What time is it? is sort of
Which is the hour? when asked in Spanish, so you are identifying one of the 24 moments in which we have divided the day. We are not identifying a property of time, but one segment of the day.
The same way we don't say
qué es tu nombre si no
cómo te llamas for
what is your name we don't ask
what time is it? as you do in English but sort of
which is the hour? or
which is that moment of the day?.
We also say that
Era por la mañana cuando me encontré con Pablo.
Es a mediodía cuando el sol está mas alto y cuando oscurece es porque es de noche.
Ahora es de noche.
We are picking between the segments in which we divided the day, not a property that happened to the day.
The only time you would hear that the tiempo está is to talk or ask about weather, not time, and for the reason you said (mutability).