The patches are much smaller than they used to be, but they're still an obstacle to updating pip. See #981 for details of the remaining patches and our previous attempts to remove them.
Once we're able to use an unpatched version of pip, we could in theory stop bundling it with Chaquopy, and instead install it into a cached venv during the build, as build-wheel does. But I don't think this is a good idea, because we would still need the system to provide a bootstrap copy of pip to do the installation, and not every Python environment provides that – e.g., Debian breaks it out into a separate package.