I can't believe it but I have had EXACTLY the same issues with my Everlane U neck tees as Jenava. Stains don't come out, and small holes develop from semi-tucking.
The best made cheap tees I have purchased have come from Uniqlo, Gap, H&M and Urban Outfitters (the $25 range ones). Zara tees are the worst in my experience. Lose their shape, seams twist, and stains don't come out. For some reason, the better the fabric, the easier it is to remove stains.
My Madewell tees are so-so, as are J Crew.
Otherwise I have purchased really nice tees that hold up well from Three Dots and Velvet. Splendid are OK, but quality is not so different from Gap and cost more.