There's certainly short supply of the secret sauce in Qualcomm's baseband.
Your team spent millions building it, and, in order to give a sufficient incentive for teams to do similar things to that, the law should probably give some protection so that Qualcomm can make a profit from it. But you're conflating a bunch of things here:
1. Qualcomm knows the product and has the engineers. Qualcomm is uniquely positioned to build usable reference implementations, chips, etc, and to charge for this service and for support. This requires no legal protection whatsoever.
2. Qualcomm holds copyright on the code base. This has nothing to do with patent law, and I think that very few people would dispute that copyright makes sense in this context. (Whether long-term copyright makes sense is a different story altogether. I tend to think that a decade or two would be more than enough to make Qualcomm's investment worthwhile enough that they would do it.)
3. Qualcomm holds lots of patents that prevent other people from spending the same millions of dollars to develop a competing product without taking significant risk of being sued. I, and many others, think that the law should not offer Qualcomm this protection.
4. As you said, the sauce is secret. I think the question of whether Qualcomm should be permitted to keep the sauce secret and how much the law should help or hinder this secrecy is worthy of at lease some debate.