Instagram API deprecation 2020
The legacy Instagram API - https://www.instagram.com/developer/ will be deprecated in favor of Instagram Graph API provided by Facebook - https://developers.facebook.com/docs/instagram-api
In order to use https://api.instagram.com/v1/users/self/media/recent/ this endpoint you need Basic permission. As documentation says, it will be deprecated in early 2020, which means that the legacy API will be most probably shut down, since there will be no more capabilities to request for.
You should most definitely start building your app with Graph API. Please keep in mind that it takes some time before you can go live with your app. It requires couple of things like Business Verification, review of requested permissions in App review and it can take some time to be able to go live.
Please keep in mind that the Graph API works only for Instagram Business type of accounts. You can't use it for regular accounts at the moment. It is not clear yet if it will be available for all accounts, but most probably it will be in the future. It was the same as with deprecating Public Content permission on Instagram legacy API. They added similar functionality in Graph API.
If you plan to support all users, you will also have to apply for Basic capability in legacy API. In other words, you need to support both Instagram API and Instagram Graph API if you plan to target all Instagram users, both regulars and Business profiles.
Another thing to keep in mind is that you can't really report bugs or get any help from legacy Instagram API. If you will find the bug you can't report it as they do not accept it due to deprecation.
So start building with Instagram Graph API, once you will be good to go, try to add Instagram legacy API support. If everything will be fine and Facebook will add support for legacy accounts, your Graph API should easily take over Instagram legacy API functionality.
Most probably the reason why they are tightening the integrations and makes it harder for the developers is user privacy. They do not want to have yet another incident like Cambridge Analytica for instance.