In general, there is nothing wrong with it at all. This advice would seem to be wrong.
In fact, by relying solely on
stoi and friends, you lose any ability to control the conversion process. You might want to use these in some very domain-specific cases where you want to extract a specific number of characters and then attempt to convert them, but that's down to business logic.
Certainly, relying on antiquated code like
atoi is even worse, what with its undefined behaviour on encountering many failure cases.