Yes. You can not easily or safely install precast lagging from the top down. Lagging should never be slid down as the site gets excavated. Therefore, you dig about 5 feet and install lagging. Dig another 5 feet and install another 5 feet of lagging BENEATH the first 5 feet of lagging, always placing the lowest board first.
Once a wall is lagged and tiedback, the deflections have already occurred. Then the finished CIP, shotctete, or precast facing can be attached to the soldier beams.
A CIP facing does not "encase" the front flange of the soldier beam. The facing is poured or sprayed against the tiedback wall and is attached usually by welded shear studs. Also, don't forget, the wall also needs some drainage system such as geocomposite chimney drains.
A CIP wall can use a form liner for aesthetics. A shorctete wall can be sculpted. A precast facing can have aesthetic details cast in. I have never seen or even read about a separate 2" thick aesthetic coating being used.
Precast panels are heavy. It is hard to make sure there is full, tight earth contact behind precast lagging, especially if you try to slide them down while adding additional panels at the top of the wall. Also, tieback anchors may interfere with sliding down the precast panels (unless you use a through-beam tieback connection detail). If you try to build a wall with through-beam tieback connections and precast lagging tucked behind the soldier beam flanges, the soldier beams may become very large which will then require large diameter drill holes which adds significant cost. In addition, the soldier beams have to be positioned perfectly to assure proper bearing of the precast against the flanges.
A CIP or shotcrete facing hides, or compensates for, the inevitable, as-built, wall discrepencies.
If (as you describe above) you are studding on a CIP facing, why would you also need to use precast lagging?????? Use wood lagging, usually untreated.