I've generally had good luck with Land's End, and I've shopped LE for decades. Literally. My now adult sons went through elementary through high school wearing LE, and so did mom. Today I mostly buy LE jeans and casual pants, and outerwear, for which they're well-known.
LE tees and shirts are good basics. Like you, I find them boxy. The fabric is usually decent quality: a thicker cotton knit than most tees today, not at all see through. I'm less sure about blouses and shirts. The ones I bought didn't feel scratchy, but I'm not super sensitive to cottons or polyesters, just wool. (LE cashmere sweaters have been good buys for me over the years, but have gotten thinner just as have most other brands of cashmere.)
I always say give LE a shot. They may have just the right thing for you. I hope this item proves to be a winner!