Compatibility is the entire reason
JPEG is the most universally accepted image format there has ever been. Any upload form, any email client, any printing service, any device with a screen will take one. WebP is better in nearly every technical respect and is still refused by a long tail of software, and that tail is exactly where important things happen - a visa application portal, an insurance claim form, a print shop, a supplier system built in 2009.
Converting is the pragmatic answer, and it is worth being clear that you are trading file size and quality for acceptance. That is a good trade when the alternative is an upload that will not go through, and a poor one when the image is headed for a web page.
Transparency and animation both have to go somewhere
WebP supports an alpha channel and JPEG does not, so any transparent region has to be resolved to a colour. Here that colour is white, chosen deliberately rather than inherited from a blank canvas - which is the difference between a logo on a white background and a logo in a black box, and the second is what most naive conversions produce.
WebP can also be animated, and JPEG cannot be. An animated WebP converts to a single still frame. If the animation was the point, this conversion is not the one you want - you need a tool that can produce a GIF or a video.
Doing it locally when the image is a document
Consider what actually gets converted for these compatibility reasons: a scanned document saved from a web portal, a screenshot of a bank statement, a photograph of an identity document, a medical image downloaded from a patient system. These are being converted precisely because they are on their way into some official process.
Those are poor candidates for uploading to a conversion service, and they are the common case rather than the edge case. Converting in the browser means the file goes from the folder you downloaded it to, to the form you are submitting it to, with no third stop in between.