Can we set minimum samples per leaf in XGBoost (like in other GBM algos)?

You could try using min_child_weight. According to the documentation, this parameter:

minimum sum of instance weight (hessian) needed in a child.

For regression problems with MSE loss, the sum of instance weight will result in the minimum samples per leaf node because the second derivative of MSE loss equals one.

For classification problems, it will result in a different metric that characterizes the purity of the samples in a leaf node (e.g., for binary classification, if a proportion of samples of one class heavily dominate the other classes in a leaf — there is no need to split it further).

I don't know about a specific reason for not having min_samples_leaf parameter. I guess its interference with min_child_weight will bring some design challenges and confusion to the users.

xgboost has min_child_weight, but outside of the ordinary regression task that is indeed different from minimum samples. I couldn't say why the additional parameter isn't included. Note though that in binary classification, the logloss hessian is p(1-p) and is between 0 and 1/4, with values near zero for the very confident predictions; so in effect setting min_child_weight is requiring many currently-uncertain rows in each leaf, which may be close enough to (or better than!) setting a minimum number of rows.