My identical twin girls were together in the first year of kindergarten (2-3), then split at age three for next 3 years, now back together at primary (started age 6 going on 7) for organisational reasons.
The split at kindergarten was hard for them at first, but ultimately very positive for their personal development. One of them used to act as the "social secretary" for both, but in separate groups (albeit with regular interaction throughout the day) her sister learnt to forge social contacts by herself.
However, having said that they are very happy together in the same class at primary, and both are thriving socially and academically. They tend to have largely the same friends, but then that applies equally to other close-in-age siblings we know. For some reason the combination of DT and an only-child friend of either sex seems to work exceptionally well.
Now 8, they both dislike the suggestion of separate bedrooms, classes or out-of-school activities. On the other hand, they will happily do their own thing at home or join in with different groups of children at school or in other social situations. They separate when they want to - we do not impose it on them. They are both pretty self-sufficient characters, in many cases more so than their peers.
IMO there is no such thing as one size fits all for twins, just as there isn't for other children. I defy anyone to say identical twins don't have a unique and special bond though. They absolutely do.