The system in it self would be an improvement to the game, but current rep/murdercount/criminal systems would likely hamper the design, unnecessary loss of rep or gain of murder counts due to being a group or encountering a group, pure murderhobo players could entirely ignore any threat to their rep/murdercount while bounty hunters will likely not want to fight allies of the criminal if they are blue.
People don't generally play solo, and this does seem to encompass the solo idea entirely, and when I say that, I don't mean it won't work for groups, but I foresee groups of ppl grabbing the stone, maybe following one bounty at a time either finding another group or a solo gank, then following the next guys stone.
Depending on the rewards this may not be efficient to be done that way, and if it isn't comparable to other methods of farming, it may not be preferable to do at all; In that case people will grab it to use while they are doing whatever they had planned to do before and if the stone happens to beep, then a detour will happen. IF the bounty hunters have other tasks to complete (farm gold, mats, etc..) otherwise it may work as intended.
Back onto group gameplay in regards to this, i love leaderboards, i love point scores, but I also love sections, what's stopping there to be a guild section for those protecting the nation, a guild section for those killing members of a nation, right now we have mainly tindremic and khurite nations with reputation, and there is no reason to not "fix" the flaws in the current system while implementing these types of mechanics.
Areas of the game should be properly chopped out via coordinates and flagged as nation or wild, spawning in or at priests should have no effect on reputation scores, karma based on killing "innocents" imo is fine to track via the murdercount system and effect what kind of priest will respawn you, reputation should be lost upon criminal acts in a nation flagged area, which causes the bounty system to up your score for you individually and for your guild in that nation flag, this can give incentive for guilds to not want certain types of characters running with their banner, this can fix issues with reputation loss fighting blue members of a guild whom you hold a bounty for their red player member, the bounty/stone due to the player being guilded should encompass the entire guild as a criminal while the bounty is active, that way unnecessary reputation loss for bounty hunters will not occur.
/edit: for the last part of the above, if you are in a guild and grab a bounty I think there should be similar mechanics to the individual part wherein your guild should be able to fight with no flag issues the enemy bounty\guild with no reputation loss. This should literally be a type of wardec based on the nations contract that you and your allies whom have been entrusted this job can do with no repercussion to your rep, otherwise it will not work. Or some other solution to either hamper the idea of "blue" allies of the bounty from causing rep loss during a hunt.
As you successfully kill bounties, you and your guild should gain standing in this system on the player/guild board, this would give more renown to a group or player and provide more competition, aside from monetary rewards this can bring about different treatment or available content rewards for players and guilds.
It doesn't have to look like this but this outlines more of how the system currently works and what it could look like, this could entirely fix up the nonsense of the current reputation system and actually give meaning behind current functions in game asides from just parcels.