Computers won't ever generate that number in a range of [1, 2^256], even if it's random, because it doesn't look random.
There is exactly the same chance of it generating 827 as there is of it generating any other number.
Would you feel more confident if you had the dice rolls hashed by HMAC-SHA?
But HMAC requires a key and a message, which you don't have with a simple series of dice rolls. And no, I'm not suggesting we should use HMAC instead - I'm simply pointing out that there are gaps in your (and my) knowledge. When we often talk about not using closed source wallets because we can't know what they are doing, and we often talk about not coming up with your own encryption scheme for your back ups because you will almost certainly come up with something inferior or lock yourself out of your own wallets, then it doesn't make sense to advocate coming up with our own entropy generation schemes when we don't really understand the intricacies of what we are suggesting.
A lot of full time cryptographers have spent a lot of time working on methods to securely generate entropy. I'm not crazy enough to think that I, with no formal cryptography training, will be able to come up with something better.