There would be nothing wrong with that, but unfortunately development companies often take advantage of people's ignorance and try to confuse PWAs with full-fledged mobile apps. They argue that PWAs can go offline or send notifications. Unfortunately, in practice, PWAs have significant limitations, especially in user-friendliness, ease of distribution, etc.
PWAs are thus suited for very specific, often internal corporate purposes. In the vast majority of cases, it is not suitable for widespread commercial use.
The imaginary nail in the coffin for PWA applications was put by Apple, which threatened to stop supporting PWA. Under pressure from developers, it eventually kept the feature in iOS. However, it is not at all certain that this will not change in the future.
For more information, see, for example, this article on Macrumors.
Of course, we at Pixelmate also develop PWA apps. In specific cases their development makes sense. However, we have been trying to fight against the marketing claims of some developers that PWA is basically a full-fledged mobile application. An ignorant client may then get an app that no one will want to use in the real world.
The decision of whether to develop a PWA app or a traditional mobile app should be made after careful consideration and a good understanding of all the fundamental flaws that progressive web apps have over mobile apps.
Do you have an idea for an app? Write and let's discuss it together.