I have three suggestions.
Suggestion 1: Hiding Discovery Tags
The tags to me are a marker signifying that at least one player has been this way and lived to tell the tale. This can be interpreted many ways. Firstly, someone has beaten you to an extra exploration payday that could have been yours, and secondly, someone has a mark etched on the Universe that nobody else (save the devs on a particularly bad day) can ever take away.
How does this affect exploration? Are they warning posts to look for other places to go? Is finding a bunch of tags all with the same name reassuring, that you're following a path that is safe to travel so keep going, or discouraging that you got there too late and telling you to go find something else? And if the latter case is true, then where should they go?
A while back I suggested that the system map have an option to hide discovery tags. I still think, while it gives a false impression of the situation, it will encourage others to see that there are places to visit, as finding discovery tags on one's journey might lead to a sense of anticlimax for the aspiring explorer. The global statistics and discoveries will of course always be available.
Suggestion 2: galaxy map view of known and explored systems
A further step in the right direction is in having the galaxy map display a colourful galactic overview of which systems are known to the player's own personal map through map purchasing, visiting, discovery scanning, or detailed surface scanning, and to which degrees these are the case per player (as dictated by different coloured dots). I think that letting the explorer just go to systems that they themselves know they haven't been to or fully detail scanned before (regardless of their first discovery status) would be more of an encouragement to them.
Even better, personal map sharing can become a thing, with the galaxy map showing at a glance which systems CMDR Alpha Juliet has visited alongside which systems CMDR Zulu Romeo has seen. In fact, it could work out as a better system than the first discovery system in terms of following another player's journey, although it must not replace the first discovery system. There can be separate overlays per CMDR depending on how many maps you own. Of course, the maps of other CMDRs are only as complete as what they were when you obtained them, and will not update in real time, but your own map will for you. It will not stop you earning new data for systems you haven't seen yourself, though, or bagging discoveries on systems the other player hasn't got despite passing through. It's just a guide to compare notes as it were.
Plus, by showing a galaxy map overview of systems visited and proportion of data collected, promoting the buying and selling of maps and regions, and enabling map sharing, it reinforces this notion at present (or as I see it) about exploration data. As I see it, all system data explored and learned is bound to you, the player, and not your ship, and is learned immediately and permanently. If your ship is destroyed you won't be able to profit from selling your data and earning first discovery tags (as nobody believes your tale) but you still keep the data of where you have visited and what you have scanned. This way, emphasis is placed more on knowledge rather than wealth and fame.
Suggestion 3: more detailed Universal Cartographics debriefing
Hiding the tags on the way out might give a false impression of the situation that only selling the data will reveal, but to me, in my mind, exploring to gain data and selling the data for credits are two completely different mindsets. Personally, maybe I'm getting weary, but knowing that I have a bunch of first discoveries or not according to the UC popup isn't a big deal now, and certainly I don't see them as extra credits for me. Sure, there are one or two systems on which I am proud to see my name in lights there (OK, there *are* two that I care about

), but after a thousand system journey with hundreds of bodies tagged by myself come the selling of data, new discoveries tend to blur into a lump of letters and numbers.
If UC have a way of showing you the appearance and description of the exact bodies scanned so you can remind yourself of what you scanned, instead of a breakdown of the value of the individual bodies only, then I might care more about which new systems have tags on them come selling.