I voted yes for everything. However, with the exception of leagues, I think that they should be restricted in some way, at least most of the time. For example, the current WC rules are a good example of how to do shards. You can use them, but they cost you some upgrades. In tournaments, in the time I've been here, there was a shard of serendipity tournament, and a shard of gratitude tournament, where those were legal, respectively. The first didn't have any restrictions around the shard itself (I think you could only use cards with random effects, like fate egg, mutation, dusk shield, pandemonium, etc) but the second had some sort of card limit and a forced mark of life based on the number of shards you used.
War is going to be a lot trickier to balance the shards around. In most other events, people can choose from any of the 12 elements, so one element having a far superior shard doesn't really affect much, but in war, it makes a much bigger difference because of the elemental loyalty. If a way can be found to properly balance shard use in war, I'm all for it, and would encourage their use, but if not, I'm ok with shardless war as well. I'd also rather not see it limited to something like one shard per deck, because that would increase the luck factor too much. (Oh, look, the death guy just topdecked his lone SoSa... lol) I don't have any suggestions on how to do it, but if a balanced method can be found in war, I think they should be used. If not, then that's fine, too.