The Reward Pool is the Reward Pool, it does not get bigger or smaller by adding more activity. So yes you are absolutely right there is zero problem. Personally, I totally agree with your PoV, but let me state the standpoint of the 'HIVE' Society as I can observe it.
Your scenario raises the philosophical question of value, work and online 'being'. There is an ongoing conflict of interest about the Proof-of-Brain and what shall be rewarded to what kind of extend. Only extremely far developed societies do even debate and implement systems of checks-and-balance for the purpose of appropriate behavior as a member of a high culture society. In my scenario 'the 1-Account User' can be considered as an uprising member of the society, in your scenario it is more difficult and people will come to different judgements. Now to finalize this strain of thoughts, for a society it's good to get a lot of people behind a common idea and to respect each other’s sense of value. For personal Freedom it’s necessary to follow set rules as they are: ‘Don’t harm no other and don’t take no shit’, therefor being a member of society means giving up personal freedom – consistently. It’s a tragedy, you need to be right without insisting on getting it.
@lukestokes (whom everyone should follow) shared some his thoughts on working entities inside online ecosystems in the recent weeks and month. He asked whether any Human or KI that is doing some sort of valuable work, therefor exists as such being of power and value? I tend to believe you're on the 'yes' side of this question.
Hope you have a nice day.