I'm not sure you realize how hurtful your comment is. There is no beg screen within the extension, and open source developers who seek funding for their projects are not beggars.
The donation page is shown during the 30th and 100th use of the extension. That means the page is shown twice during the lifetime of the extension. Showing a donation prompt is the only effective way to let users know that there's a possibility to support the project.
When the prompt was not shown, the extension received no funding at all, despite the usual contribution links being present in the appropriate places. Users do want to support their favourite extensions, but most of them do not find out that there's a possibility for it, unless they are informed during the use of the extension.
One alternative would be to start charging for the extension, which would bring in substantially more funding for the project, but that would prevent people from freely enjoying my work, and for everyone to benefit from it regardless of their socioeconomic status.
Some projects bring greater value for society when they are freely accessible for everyone, without locking advanced features behind a paywall, and without compromising on user privacy, while being partially subsidized by users who can afford to sponsor such projects.
There's also the possibility of Mozilla introducing new features for users to seamlessly support the development of extensions right from their Firefox accounts, but instead of working towards that goal, several features related to contributions have been deprecated on Firefox Add-ons.