So I can't *entirely* explain why, but I believe this fixes#13132. 🙈 I basically ended up looking around at other `_next` URLs (are those asset URLs?) around the project and seeing that they tended to use `delBasePath()` to remove the base path from the current page's path whenever it was used.
When testing locally with the [repo submitted with the issue](https://github.com/robertovg/next-base-path-example), I no longer experience the constant page-reloading in dev mode when adding a query string to the URL.
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