Starting with the “workaround”…
Each recipient that is prepared to receive unsolicited files via AirDrop merely needs to add you as a Contact within their own Contacts App:
Add and use contact information on iPad - Apple Support
For you to receive AirDrop files from yourself, if you haven’t done so already, you will also need to create a Contact Card for yourself - with one additional step. After creating your own Contact Card, access settings:
Settings > Contacts > My Info - from the list of contacts, find and select your own entry*
(*) when selected, you will see “me” against your name - both from the picker - and in the Contacts App itself.
Next, AirDrop settings are set to allow AirDrop to Contacts Only:
Settings > General > AirDrop - select Contacts Only
Now to address your complaint and observations…
AirDrop was fundamentally changed some time ago in response to many complaints from Users that were receiving unwanted/unsolicited photos/files via AirDrop. Many (if not most) Users were habitually leaving AirDrop set to Everyone - allowing receipt of unsolicited material at all times. When set to Everyone, as you observe, your device(s) will accept data from any Apple device that is within range.
To illustrate a typical scenario, imagine a crowded railway carriage… anyone with an Apple device can “see” every Apple device within ~30m that has AirDrop enabled (likely set the receive from Everyone). Each Apple device will identify itself by Name, which in all likelihood will be the persons name - which may suggest or fully identify gender.
In this scenario, consider a potentially male Apple owner with nothing better on his mind than mischief. How better to “entertain” boredom than to send a salacious photo to another Apple user within range - and see their reaction when they receive and open that photo? Now consider the reaction of the recipient - very likely female - when they receive that unsolicited photo? Having been watching the passengers, our protagonist may have seen the reaction - and may escalate the game. From here I’ll leave you to join the dots leading to harassment or worse.
In addition to the described scenario, AirDrop could also be used as channel to deliver malware or other exploit to devices.
Apple responsibly responded by modifying AirDrop. As before, AirDrop can be unconditionally disabled, or set to unconditionally receive files/data from known recipients (with entries within the Contacts App) - but changed the Everyone setting such that it can be intentionally enabled when required. The Everyone setting, when manually enabled, is time limited to 10 minutes before it will return to only accepting unsolicited files from known Contacts.
In conclusion, when setup correctly on both sender and receiver sides, AirDrop can be used exactly as you perhaps intend without reliance upon the Everyone setting. The Everyone setting must be manually enabled when required - this being in scenarios where the recipient is concisely anticipating receipt of files via this mechanism.
