You don't use 3rd party software to generate the wallet. Electrum, Specter, or another FOSS app can do it fine.
The keys have 3rd-party software, but all they do is sign. Don't have a quorum from the same manufacturer. If it takes 3 signatures of 5, don't use 3 from the same company.
By that logic, nothing can ever be secure for any reason. We should all abandon the internet and go home.
From the string of your comments throughout this conversation, you seem to be making some weird, "I can't do it, so nobody can do it," false equivalency.
I don't know you from anybody, but I'm reasonably confident you're not more intelligent than all the highly incentivized people who have been, on the one hand, solving these problems against adversaries on the other hand who are every bit as incentivized to unsolve them.
None of the points I've made have been in any way groundbreaking or insightful. They're basic "I spent my free time for a year going down the bitcoin rabbit hole" stuff. You're throwing out incredibly basic objections as though they somehow mean the whole system is an unreliable fraud, but all it's really showing is that you haven't done even a cursory overview of the topic.
I'm really not trying to be rude here. People can understand code, even lots of it. People do understand it. They even understand the high-level cryptography these systems are built on. You might not, but that doesn't mean nobody does, much less that nobody can.
OP explained this, if the signing is required by multiple 3rd parties then you’re good. You can do this with pencil and paper btw and write down keys. It’s not far fetched.
I don't want to be rude, but you're not the only smart person who's thought of counterparty risks. There's tremendous incentive to all sorts of people to break the cryptographic security that secures these networks. And, thus, also incentive to stay ahead of those people.
I'm not very worried about the cryptographic security of the Bitcoin blockchain.
I am worried that in 5 years we will learn that some hardware wallets used side channels to transfer bits of your private key out to make it easier to guess for someone who worked at the manufacturer.
But you can check this. You can monitor whether info is leaving on other channels. And you can sign on an air-gapped computer and transfer only the signed transaction hash (never the privkey) to a connected one to broadcast. You can do all but the actual signature with open source tools.
Just because you haven't taken the time to learn how this stuff works doesn't mean there aren't thousands of incredibly intelligent people who have been working on it for a decade and have actually solved the low-level concerns you have.
If you use software by a 3rd party, we are back to squear one.