If I were to ever generate a seed like that, I would throw each die many times before to satisfy my own curiosity and see if I can notice patterns that shouldn't be there.
Simply noticing a pattern is insufficient to exclude bias. If you roll your die 60 times and get 15 ones, is that biased, or is that random chance? As I mentioned above, you need to use proper statistical testing, and even then you can only approach a confident limit and never exclude a bias 100%. I've outlined the process more in this post:
https://bitcointalk.org/index.php?topic=5395587.msg59967945#msg59967945.
You need to decide how much bias is acceptable to you, and how sure you want to be you have excluded it. The number of rolls required exponentially increases as you want to be more certain you have excluded smaller biases.
In that case, wouldn't 100-200 rolls with 10 different dice (even if biased) be enough to generate randomness of somewhere between 130-200 bits of entropy which is more than enough as you don't get more from 12-word seeds and bitcoin private keys anyway?
Maybe. Maybe not. The numbers given so far in this thread discuss the Shannon entropy, but have you calculated the min-entropy you would achieve from doing this? What randomness extractor algorithm are you planning to use to turn those dice rolls in to usable entropy? How are you converting those dice rolls to binary without introducing modulo bias? It's not as simple as just "roll the dice more" - it's a very complex topic which most people do not fully understand (and I do not profess to either), which is why whenever the topic of manually generating entropy comes up, I always suggest von Neumann's coin flips to simply, quickly, and most importantly
verifiably generate 128 or 256 bits of
provably unbiased entropy.