The answer is pretty much what Crypto Ghost mentioned: Apple’s security policies limit third-party apps from automatically forwarding texts on iPhones. The native options are limited to iMessage forwarding within Apple devices and iCloud sync, which require user permissions.
For any broader control or management—like monitoring texts across family devices—you’re looking at specialized solutions, and, yes, Spynger is one of the few tools that can do a decent job within OS limits. Just keep expectations realistic: iOS doesn’t make this easy, and there’s no magic workaround for real-time forwarding without Apple support.