What are these drawbacks in your opinion?
Progressives have SOME slop/movement of the toolhead, except the Hornady LnL AP ** (no toolhead) and perhaps the Dillon 1050 (never checked it out). The quality Progressives take some steps to reduce or compensate for it. But the design of the Lee turret allows much more play than most. Unlike Progressives, since only one die is in use at a time the upward pressure of the ram tilts the toolhead/die towards the center of the toolhead. (In the extreme, think banana-shaped cartridges.)
The Lee powder measure is acclaimed by some for accuracy with certain powders/loads, but most people find (insert-brand-name-here) Powder Measures are more accurate, easier to use, and spill/spit less powder.
Many people can get the Lee on-press primer system running smoothly, but many more give up and hand prime.
Having said all that, the Lee Turret is where I started and it certainly produces ammo lol. When I wanted precision rifle rounds and couldn't maintain tolerances, I went to a single stage press. When I needed higher throughput for pistol, I went to a Progressive. The Lee Turret is not a bad starting point, and for many its not a bad ending point either.
I mentioned that the Lee Turret had the same drawbacks in turret or single-stage mode because OP wanted to use ss mode tomake precision ammo on the turret. If his concept of precision ammo includes concentricity and consistent adherence to OAL, etc . . . he isn't going to be happy with a Lee Turret. Better to start with a single stage.
** TBF, the LnL AP can develop some slop in the bushing, which is corrected by replacement, or by shim.