If you used Parity because it has 1,700 stars on Github and was written in Rust, you're doing it wrong. Stop. You can't assess merit based on what everyone else is doing. The only hope in a situation where you don't know what you don't know is to stick with fundamentals. And even then you could still get burned. But that hasn't happened yet, which is why it's the least risky move.
It will take at least a decade for the cryptocurrency ecosystem to stabilize. Why risk anything when you don't have to? Arguing "I don't use the Bitcoin Core wallet because it's less convenient" is exactly that: an unnecessary risk. If you're set on jumping into this world, at least do it safely.
I know you got burned in MtGox, but this has nothing to do with third parties or storing assets in some insecure manner. This is a fundamental issue with Ethereum and its community.
If you want to be safe, don't buy an asset that's being protected by a couple of young and naieve idealists that just care about putting their ideas on the market.
This feels like a good opportunity to point out that a big part of decentralized infrastructure is that there isn't a 'First Party'
You've veered away from your original statement towards one that I don't disagree with. Of course you shouldn't just trust any software you find on the internet. That's not the same as "only trust Ethereum core". Slandering "third party" as if that has any meaning is silly. You should treat everything on its individual merits, including the Ethereum reference wallet.