1. Kid A plays with Kid B
2. Kid A plays alone and Kid B plays alone
As compared to a three-child household: 1. Kids A, B and C play together
2. Kid A plays with Kid B, Kid C plays alone
3. Kid A plays with Kid C, Kid B plays alone
4. Kid B plays with Kid C, Kid A plays alone
5. Kid A, Kid B and Kid C all play alone
So, in a bigger family, many more communication patterns between children can arise, which, among other things, might develop the child's empathy etc.Adding mom and dad as "players" would give us many more possible scenarios here (Kid A playing with mom, Kid B alone or with dad, etc).
I'm a father of two with a low income, and I would like to have a third child for precisely the above described reason. As a sociologist in my country put it -- somewhat harsh words maybe, but probably largely true: a single child might get spoiled, two children may start competing too heavily, but three children and above is company.
And yes a lot of interaction, but it doesn't guarantee anything further down the line - when long time adults youngest is still spoiled and selfish and not really a pleasant person to be around with for anybody, including siblings and their own mom. Middle one is scared to have kids, a decision that she may end up regretting later easily. And my wife is also carrying her part of the burden, won't bother you with details.
The grass is always greener behind the fence and all that.
On a personal note, I never had much positive interactions with either of my siblings, certainly not as children as not now that we're in our 40s either. Lots of fighting, absolutely zero closeness or positive feelings.