Well, there's always the option to export to a new folder. That's what I'd recommend.
But it would be nice if there were a checkbox or a button within that first prompt, to "apply to all" or "replace all". (BTW, is this an HTML export, or a different type of output?)
You could request something like this using Adobe's official feature request submission form:
html + images export.
I notice the prompt appears for each image, but not for the HTML.
That is true. Only the first html file (if that is what is in the filename input) will be asked about if there is a conflct. However there is still the problem of having to confirm all of the images one at a time.