That depends on the hash table implementation and the distribution of the integers.
For the commonly used hash tables with prime size that use modulo to turn the hash code into a slot index, an identity hash for integers is usually fine (unless many integers are multiples of the prime size).
But other hash tables use power-of-two size to replace the modulo operation with a faster bit-and operation. Now an identity hash for integers is much more problematic, e.g. if all integers are multiples of 1000, only 1/8th of the table slots can be used.
The latter kind of hash tables would like all bits in the hash value to be well-distributed; and this is typically not true of the underlying integers. So an additional mixing operation needs to be used. Whether that mixing happens in the hash function or in the hash table depends on the implementation (for some, it's even configurable, e.g. is_avalanching marker in ankerl::unordered_dense).
