I think what you are describing sounds basically like some combination of observation fields and projects and/or a third-party app built on top of the inaturalist platform/using the naturalist API. The platform itself is pretty mature technologically, supports a lot of use cases, and doesn’t really have the resources or inclination to implement taxon-specific ID solutions. There is some discussion of various third-party apps here: https://forum.inaturalist.org/t/3rd-party-inaturalist-tools/25971/13
The other thing you are talking about it encouraging users to take better pictures or relevant features. To an extent, that is actually baked into the computer vision apps like Seek; they are meant to encourage decent photos in part by providing more a useful ID when the photo is decent. That feature could certainly be improved further, and playing with iterations of that is possibly another good opportunity for third-party app development. And of course, communication with IDers can help users take better pictures.
The site also supports copy-pasting an entire DNA barcode into an observation field. That feature is mostly used in fungi right now. I don’t think the site would ever allow it to directly affect the RG status-tier of an observation because it is not something that can be checked with citizen science.
What external projects can/have done when they want a bunch of physical samples or DNA barcodes or whatever is to organize some kind of event in which the project organizers provide citizen scientists with a shipping address/label and sample collection/preparation instructions (or even a sample collection kit!) to send samples to in exchange for having their name on the eventual paper or whatever. If a project really wants those DNA analyses done they will have to pay for them themselves though; that isn’t a reasonable thing to expect citizen scientists to do. Obviously, care must also be taken to ensure that whatever sample collection and shipping you are asking citizen scientists to do is legal, ethical, and ecologically sound in their jurisdiction.
This kind of thing has actually already been done to an extent for taraxacum papers in North America: for example the data in Genome size variation among common dandelion accessions informs their mode of reproduction and suggests the absence of sexual diploids in North America was based on dandelion samples collected and sent in by volunteers in North America (though not organized through inat, as far as I know). I could imagine a larger or more detailed physical specimen collection project like that in combination with a set of associated observations posted to inat could be an interesting paper for someone to write. And I’m sure you could recruit a decent amount of volunteers even just from these forum threads.