I don't play in solo, but I would guess that the solo player is there solely as they are playing the "single player" option, rather than banished there by 'nasty gweefers', your proposition would remove that option entirely, fact, so those who have elected to play alone, would be either 'forced' to accept a play style they have no interest in, or to stop playing altogether.
Perhaps a 'solo' player could reduce dramatically the chance of an encounter with other players by playing outside of inhabited systems, but even if they have a passion for deep-space exploration thay would still have to return to a station to off-load accumulated exploration data and complete any repairs, and at that time could encounter other players... The proposition, even with your caveats, does not permit a 'solo' player to continue to play as they wish.
Not entirely no, that is true. It's a problem the player would be tasked with addressing themselves, which is how I think it should be. These new problems give rise to more player agency, more room for imagination, and maybe demand for new cool additions to the game to serve as tools.
Example. I like to pirate player cargo ships.
I'm immediately faced with the fact that I need to use specific in game tools to accomplish this, and must also find somewhere that offers what I want to do.
I do not have some button to press and make it happen. So that means I have to make ship build choices. These choices mean that a dedicated PvP ship will out do mine should I try to face it. So I'm faced with how to confront that problem too. The onus, to deliver the experience im seeking within the sandbox, is on me. I argue that should be the case for everyone.
So solving the desired player experience of wanting to be alone, should be on the player. It also opens up potential for new tools in the sandbox (which I have tons of ideas for too as I imagine everyone would) to help the player thrive in it via smart ship choices and decisions.
Like I've said previously, the problem would be better solved through game mechanics than modes, and the existence of modes means the problem no longer exists to be solved.