But consider what would happen if Bagoas were present when the fleet ran into a fight. The trierarch led the ship in war, just as the pilot navigated it. It was a real role in that circumstance. Alexander could not afford to risk confusion over the command in a battle situation. I would not press this point too hard, because you might suggest that Alexander ensured that Bagoas never went aboard his ship(s), but I think that creates a certain awkwardness that Alexander would have sought to avoid in the first place, had it been necessary.
I think that you are assuming here a) that the Indians had ships capable of river warfare and that they engaged in such, and b) that there were any cities close to a wide river, with a tendancy to flood, that needed attacking by water. With the army on both sides of the river, it's unlikely that there was any water-borne fighting.
In any case, it is probable that the fleet was reorganised either when Craterus went westward or when they reached the delta. While exploring the delta and not in close contact with the army, the bulk of which might have been left at Patala, the fleet would probably have come under Alexander's direct battle command and been manned by marines. When they reached the sea, it probably passed to Nearchus's command, a Cretan sailor, as it would seem unlikely that there would have been any high-ranking Persian with naval experience who would have accompanied Alexander this far. They are far more likely to have been left in their field of expertise in the Mediterranean.
The onus is on you to explain why Alexander's Bagoas should have been an exception. Beware: if you say he was too young and callow, I shall mention the Royal Pages
We know that eunuchs fought and hunted but that they lacked the strength of full men. Given that Bagoas was a young man, a eunuch, and a dancer, he is likely to have been slightly built. How long would he have lasted as a soldier in hand to hand combat?
Actually, I think the onus is on you to explain why exactly you think that there is any difficulty in a high status individual giving a public performance. The counter examples are legion in both ancient and modern times. There's Alexander's own lyre-playing, Nero's various performances, Commodus and his gladiatorial exploits, Madonna and her shows, Condoleezza Rice with Aretha Franklin... Do you have the same issue with these cases or have you read one too many of the strange 19th and early to mid 20th century books on Alexander that insist (quite bizarrely) on retrospectively applying Victorian morality to his world? (Obviously, I know you read them in a good cause and we appreciate the insights that you bring to Pothos from their pages, but please don't let them get to you. We value your independent views too highly
I think you are being somewhat unfairly antagonistic here. The Carmanian incident was a competition, it was not a PR exercise, it was not a one-man show, it was not a carefully staged competition which the emperor had better not lose. It was a competition which Bagoas appears to have won fairly. True, if Alexander was one of the judges he may have been biased, but there is no hint of this.
The point of the Carmanian incident though was that Alexander kissed Bagoas in public. Is he likely to have risked treating an army officer as a boy in front of men he might have been leading in battle? They are hardly likely to have much respect for him if Alexander did. Even if they had affection for him, they are more likely to have considered him a mascot.
The kiss was also at the insigation of the army, which argues that they were well-disposed towards Bagoas, and that they enjoyed his performance. Thus they, at this stage at least, would not appear to have seen him as a threat included in Alexander's Persianisation of the army. Even if they were indulgent towards a young, comparatively inexperienced, and perhaps in their eyes a toy soldier, as an amateur dancer, would he have had the time to reach a standard to compete against professional dancers and beat them?