It needs to not just be better. It would need to be better in ways that aren't achievable with the alternative, and sufficiently better that it justifies the cost in terms of space and management requirements imposed.
Sure, and different people make different trade-offs. I don't like using mobile websites, because to me, the interactivity when it comes to touch/swipe/zoom interactions, or edge-swipes etc is always a little janky compared to a proper app. If its a website that I use a lot, I'd rather just have the app than deal with the mobile website.