It’s very situational, and often doesn’t really fit in. When it does work, though, you need to see the moment and take advantage. Then you feel like a mastermind and it’s fun.
As a general rule, I like to have 2 dinos in my squad with swap-in effects. This makes pretty high odds of all 4 dinos being useful. I’d rather have 3 champs and Stygidaryx than 4 champs that are all useless swapped in during battle. If you just have the 4 champs that can’t swap, you might as well only have 3.
I’ve never heard good things about starting with Stygidaryx, but honestly, I don’t think it’s a bad plan. It’s not going to be more helpful if you don’t start with it, so why not? It may not seem to do much, but it can take a hit. It’s durable for a flier. If Stygi doesn’t like what she sees on round 1, she can swoop out instantly. Even if it’s Erlidom, Stygidaryx will survive.
I have found I like starting with Stygidaryx especially when there’s another dino right after it that’ll be fun to swap in. Take the Suchotator, for instance. Stygidaryx uses Cleansing Swoop to the Suchotator, who’s a friggin’ tank of a bleeder. Suchotator then stacks the bleed on the next target and survives the round after with distraction. Target’s down, Suchotator’s still standing. Also works with Thylacotator and a decent number of other beasties.
I also use Stygidaryx to time out my attacks later. I can predict when the enemy’s sick & tired of my Stygidaryx and will use Thor’s rampage to make sure it goes down. Then Rampage is still on cooldown for when Maxima takes the field or something. Fun stuff like that. You’re just chucking Stygidaryx as wimpy tribute at that point, but hey, that’s a use.
I suppose you could also use it as a repeat blocker against Indoms. Swap it in, block the hit, and then Cleansing Swoop can swap it back out the very next round. Try that with Dracocera. I could see that getting annoying.