Im sorry i type such large messages, am a touch typer and i ramble on, often.
IIRC tent caterpillars only eat the foliage of the plant they were born on, wandering ones do no harm to anything. Put them on a plant they weren't born on and they don't even know what to do lol.
Most the wandering one's you see are already doomed unless they can find their way back o the same species of plant they hatched in. It's kinda bizarre though. They can be hatched on just about any tree or shrub, and thats the one they stay eating. If hatched from a tent on something man made (rare, but does happen) all those caterpillars starve to death usually, unless they fall out of the tent onto foliage, then thats what they'll stay eating.
They only problems they really create here are the mess when you step on them after they hatch in thick. Most of the time they end up in very large trees that can more then handle a tent or two, but they do end up in my moms dogwoods and goldenrods sometimes. When that happens we do indeed spray the tree.
They make insanely good fishing bait too. A lot better then nightcrawlers. The birds i see eating them most here though, are usually mockingbirds and Robbins, both species im quite fond of. I've seen the killdeer get em good when theyve fallen to the ground.
Wouldnt surprise me if tent worms take out entire old growth trees in a month up there. Its so warm so quickly in spring down here, and foliage so dense from canopy to floor, theyre only around for a week or two before they disappear to become moths, and a week later you cant even see any evidence they were ever there besides the old washed out tent.
I like tent caterpillars a lot more then i do blue jays. Personally lol. They can tear up a tree/bush pretty bad if its small enough and a tent gets pitched in em though. But they dont swoop at me or sh*t on me while yelling at me either...
What i've actually done most with tent caterpillars if i find a tent i can get to early/easily enough, is toss em in a jar full of host foliage right as they bust out of the nest. And let my nieces/nephews raise them into little moths. Great tools for peaking an interest in nature/biology/ecology for kids. Them and tadpoles both.