Well I understand a little bit more your point. But you are not the "average Joe" as you say and very few people have your skills to be able to spot weak libraries and functions related to entropy generation in software wallets. For the common user it's basically a black box you need to blindly trust. So personally I prefer sticking to known pretty reliable physical sources, even if they are not radioactive like Balthazar's stones 
I tried this and it worked very well.
https://www.youtube.com/watch?v=00h0_Tq8ThA
https://www.youtube.com/watch?v=vtk1o2Qc0u4
https://www.youtube.com/watch?v=pBdqaxtJFHQ
https://www.youtube.com/watch?v=bmK_MVnli7c
My source code is here:
https://github.com/CryptoManiac/rng
It works much faster than flipping the coins and provides a real, guaranteed and unconditioned security.
At least Ian Coleman and Bitaddress conceptors seem to agree with me.
It's certainly not perfectly random but it's safer than relying on so called "True Random" Number Generators that can be bugged or having design weaknesses, and are actually just trustful blackboxes.
If you wish a guaranteed and independent entropy then you can buy any uranium mineral and use Geuger counter to make as many random bytes as you want.I tried this and it worked very well.
https://www.youtube.com/watch?v=00h0_Tq8ThA
https://www.youtube.com/watch?v=vtk1o2Qc0u4
https://www.youtube.com/watch?v=pBdqaxtJFHQ
https://www.youtube.com/watch?v=bmK_MVnli7c
My source code is here:
https://github.com/CryptoManiac/rng
It works much faster than flipping the coins and provides a real, guaranteed and unconditioned security.
At least Ian Coleman and Bitaddress conceptors seem to agree with me.
Quote
Entropy values must be sourced from a strong source of randomness. This means flipping a fair coin, rolling a fair dice, noise measurements etc.
https://iancoleman.io/bip39/Quote
An important part of creating a Bitcoin wallet is ensuring the random numbers used to create the wallet are truly random. Physical randomness is better than computer generated pseudo-randomness. The easiest way to generate physical randomness is with dice.
https://www.bitaddress.org