I think the point you're making is, the implementation isn't "just add the icon" and/or "this could be poorly implemented resulting in noticeable additional load time at the quest counter". Let's not pretend like either of us have knowledge of how PSO2's client, server, or database are designed, or assert there will be an undesirable client side effect. I/we are not developers on the PSO2 team and are in no position to determine whether or not this could be implemented as a QoL improvement without adversely affecting current performance. We can leave that up to the development team and just say 'I think this would be good for the game and its players'. The point of this section is to provide feedback, and let the PSO2 team determine if it's worth investigating.
It's 100% OK for community managers to come back and say "We think you have a really good suggestion, but there are technicalities that prevent us from implementing this in a reasonable manner" or "We've thought about this and are not doing it". Who knows, the suggestion may even become triaged with a higher priority than we'd expect. There may already be plans for something like this in the future. We don't get to see their backlog, so there's no way of knowing if this idea has even been a twinkle in someone's eye in the past. I thought it would be a decent way to eliminate the annoyance of searching down the AQ list for parties one at a time with no indication of whether any parties were even doing the mission on the ship. If a players options are to either do that search or log off and do something else, some will choose the latter - and that has a more concerning adverse affect at the quest counter.