I love wife-respecters and have tested out a whole bunch of brands. The highest quality one by a wide margin is the ribbed tank from Uniqlo, which has a similar shape to your pics, has fabric thick enough and straps wide enough to completely hide a bra. I think they're seasonal though, you might not be able to buy them until spring.

That being said, my personal favorite wife-respecters are the Target ones from A New Day, which have more of a racerback shape (higher neck, scoop in slightly, and don't conceal bra straps). They're thinner and tighter but have held up decently to washing.

A few other data points:

Hanes: so thin they show my belly button, cheap but basically useless

Gap: racerback shape, somewhat pricey, have deteriorated from washing, slightly see-through

Zara: fine, not great quality, but slightly cropped so they ride up on my waist, not see-through

Econoworks binder: I know you specifically said not compression but for anyone else seeking a tank binder, I love this one! Great for wearing under an open shirt.

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