Radial stakeout constrained from multiple, stable, back sights that surround the work, can be much more accurate than the "tried and true" setting up on a column line and cranking 90s.
As mentioned, you need very solid control network around the project. We’ve have shown on industrial metrology jobs that this control can be traversed using laser trackers. This type of control network is much more accurate than conventional optical metrology methods.
I believe, people still like the column line and cranking 90s method because it brushes over a good deal of error propagation issues, e.g., monument stability, tripod stability, instrument centering errors, targeting errors, etc.
People typically use levels for vertical control for many of the same reasons; it brushes over a good deal of error propagation issues, e.g., equipment understanding, tripod stability, instrument centering errors, targeting errors, etc.
How much does the monumentation move during the course of the day/season/year?
How do I constrain or model the monumentation movement?
How much does the tripod move during the course of the setup?
How do I constrain or model the tripod movement?
How can I better value the center of my total station?
How can I better target the item I am surveying or laying out?
Etc., etc., etc.
As you better understand your equipment Datasheet, the better you will understand the performance and proper use of your equipment.
I always recommend checking your work, especially when first implementing new procedures. Eventually your skills and confidence will increase to the point you will not feel as compelled to check “everything”. Checking your procedure will become more commonplace.
Radial stakeout, when properly done, can be faster, more accurate, more precise, safer, less expensive and easier than the older methods.