Yeah being assigned to a Hecate is probably fine.
I mean ALPHA ONE was assigned to a Hecate for most of the FS2 campaign, and the Aquitaine is usually sighted getting the hell out of dodge.
The bad fortune for Diomedes is that they happen to get killed a lot because they do risky things: they are effective enough to have a good shot at pulling it off and are expendable enough to be tasked with them.
A Hecate is kind of the exact opposite in that regard - they're too valuable to put into any sort of risk, and they're not very good at direct engagements etc, and are far more valuable as support assets. Thus they tend to be babysat by their battlegroup, and run away the moment things go bad.