Woodworking
I agree that the timbers look too square, and it's not that ancient Romans didn't have sawn timbers - they used pit saws for that. It's more a matter of whether or not they would have used expensive sawn timbers for crosses, and I think the answer to that is no. Much more of their timber for ordinary use was split, rather than sawn, from larger logs, using wedges and large hammers or mauls.
Mortise-and-tenon, dovetail, half-lap, etc. joints were the common way of joining structural timbers together right up until the beginning of the 20th century. Nails or wooden pins were often used to keep the joints from slipping apart but not as direct load-bearing members. These methods were so commonly used that historians think it's likely that the Romans would have naturally used them to join timbers together for crosses as well. The other motivation, of course, would have been to avoid using relatively expensive nails, not to speak of the fact that it would have made re-using crosses easier.
This does not mean that no one ever joined crosses using rope or nails, just that it's less likely than the joinery techniques.
Jedakk