Why binary trees? Is there any particular benefit to using binary trees instead of some higher radix?

Bitcoin stores transactions in binary Merkle trees. They take O(log2 n) to traverse.

If I used something like a ternary tree, where each node (including the root) references three branches/leaves instead of two, it would take O(log3 n) to traverse. Why not pick a radix higher than 2? Is it because of space efficiency for SPV, or something like that?