There are 2 different aspects to tenons, just as there are 2 different aspects to turnings - diameter and depth.
When work starts extending further from the jaws, a larger tenon can help, but a longer tenon can help also. HF’s such as vases with L/D > ~1 or so I use tower type jaws with ~ 1” tenon length. These are typically endgrain and are not likely to break across the grain like face grain, but are more apt to vibrate or pull out, which the longer tenon resists.
As to large tenon dia limiting the piece design, it can can be accommodated. There are different approaches. Many times I start with a large tenon and end with a much smaller one, cutting the piece down in stages.