It's hard to find good numbers on this, but one study[1] fond that well over a third uses the website (website + mobile website) and only about 20% used an app. Surprisingly, phone was still the most popular way to order. Granted, this is from 2016 and looks at
all food orders, but it shows there's a lot more going on outside the tech bubble.
I don't know how many people are using the web app, but you're going to have to do a hell of a lot better to casually dismiss my user experience report. Even just 15% or 20% increase would probably be a good ROI, as a basic webapp is not very time-consuming to write and maintain if you already have an API for the native apps (it's fine to rely on the mobile app for account management etc.)
As for the UX, if you just use the "offers for you" then it's okay, but once you want something specific (that is, you're actually shopping for something) things tend to get harder. I don't think it's controversial to say that a 22" screen works a lot better here than a tiny 5" screen.
One paper found that desktop has 111% more sales than mobile[2]. That's a whopping difference! Two explanations for this:
1. Desktop UX is better, so customers find what they need and buy it, whereas they can't find it on mobile.
2. Mobile devices tend to be used quite a lot as "time killers": something you do when you're waiting for something else. So at least some of that "40% mobile traffic" is just time-killing browsing.
Either way, reports of the desktop's death have been greatly exaggerated.
[1]: https://www.businessofapps.com/data/deliveroo-statistics/
[2]: https://www.nngroup.com/articles/m-commerce-terrible-ux/