Maybe this has already been discussed, but I want to make some points here about the possibilities of islands (i.e., disconnected graphs) with this variant.
With just two holes, it’s possible to have an island of one point
In the below board (https://shinuito.github.io/9x9board.html?neu=a2b1), A2 and B1 have been removed, leaving A1 as a one point island (even though it is not marked).
For this board, playing at A1 would either be impossible (if suicide is forbidden) or strategically pointless (if suicide is allowed). Hence, one-point islands are also effectively removed from the board.
A three point island is a gote endgame move
With three holes (https://shinuito.github.io/9x9board.html?neu=a3b2c1), you might create a three-point island
Here, one player should eventually play at A1 to secure that island in gote, so this would likely be played only in the endgame.
A two point island can be fought over by superko
We could also have a two-point island (https://shinuito.github.io/9x9board.html?neu=a3b2b1)
In this case, the players could fight a ko over control of this island, but it seems that the only way this fight could ever be resolved is for superko to eventually prevent one of the players from retaking (without making a self-atari eye fill elsewhere). I think control over this island might just go to whoever has the most territory minus group tax on the rest of the board. If the score is close enough that group tax and control over the island makes a difference, then maybe the presence of this island effectively converts the game from area scoring to stone scoring??
Starting play on this island might also behave like a ten-thousand year ko, since the first to play has to find the first ko “threat” (which can just be any legal play elsewhere).
Larger symmetric splits can lead to a fair game (0 komi)
With more holes, it could be possible to divide the board symmetrically, for example:
https://shinuito.github.io/9x9board.html?neu=a1b2c3d4e5f6g7h8j9
https://shinuito.github.io/9x9board.html?neu=e1e2e3e4e5e6e7e8e9
In these cases, White could always play mirror go to produce a tied result, so the fair komi should be zero.