Sometimes yes, clearly. It is worth ten minutes to know which case you are in.
A modern website already does a great deal on a phone, including taking payments, holding an account, and working offline to a degree. So, the useful question is not whether an app is impressive but whether it earns the extra work of two app stores, two platforms, review queues and update cycles.
It usually earns that under five conditions: people use it repeatedly, they sign in and it remembers them, it needs the phone itself for a camera or a scanner or background location, notifications are part of the job and not marketing, or it has to keep working with no connection. A field crew logging jobs on a site with no signal needs an app. A restaurant menu does not.
Where the answer comes back as a website, that gets said, and it is not a smaller project or a lesser one. Where it comes back as an app, the reasons are written down, because those same reasons are what the scope is later judged against.