As requested by @Dantelion_Shinoni, an update:
Well, maybe let’s start with the top level participation in each event to date:
As you can see, participation beyond the first hyped ones has been pretty mixed, with a few being essentially ignored complete (<100 participants) like the Tactical Destroyers and the Caldari one, and a few of the others, particularly the FFAs, faring a little better. Still, the median participation of these events is only around ~340 characters on an event day.
So basically the observations in the OP still hold - only a few hundred players engage with this feature and it is largely ignored by the player base.
Ok, so onward. Now that there is more data, I was able to better assess the effect of the Proving Grounds on activity elsewhere, and yes, there is an effect. Basically the majority of activity in the Proving Ground comes at the expense of lowsec.
To see this, first a calculated the correlation of player activity (defined as being present on a killmail) for event days and an equal number of non-event days (matched by day of the week) across the various sectors of New Eden. In this analysis, the correlation coefficent will be 1 if the number of players moves equally in the same direction each day, 0 if there is no correlation between activity in the sectors, or -1 if they move in opposite directions - that is if one increases at the expense of the other decreasing. Here is what you see:
It’s clear: lowsec is significantly impacted on Abyss PvP weekends experiencing a drop in player activity. Now, from this it is difficult to exactly see how many players Abyssal PvP is cannibalizing from lowsec. For that, I looked at the mean change in players comparing again an equal number of day-matched event and non-event days:
To be transparent, I did remove the first two events from this calculation (and their matched controls) as they were a bit of an outlier. But the data are clear: on event weekends, lowsec activity drops by about 200 characters while the Abyss PvP event only adds 340. That means the majority of the activity in the Abyssal Proving Grounds comes directly from lowsec, removing players from the open world. And if you make some allowances for queue stuffing and multibox collusion that would increase the number of characters per human player, maybe all the activity comes at the expense of lowsec.
So while that is bad, and what many people including me expected from experience with similar experiments in other open-world games, it probably doesn’t matter too much. As you get a hint of from that last chart, that decrease lowsec experienced is still quite small - maybe 5-10% of its normal activity. The reality is that even though most of the activity in the Proving Grounds comes at the expense of lowsec, the Proving Grounds are still largely ignored by almost everyone so the activity hit isn’t really significant. Even the noise in the activity of nullsec and highsec is larger than this small transfer of activity from lowsec to the Abyss.
So the main conclusions in the OP stand - the Abyssal Proving Grounds have failed to attract a player base of any size. We can now add that the players that do regularly participate mostly come from elsewhere in the game, specifically lowsec, where activity drops during the events, even if this activity that is siphoned off is very small.
Here are the raw data for your own exploration: