I suppose if someone had sensitive or protuberant nipples, then a strappy would make some sense.
They add warmth, and don’t show at the neck. Good under non-dress shirts - flannels/polos…, which are less susceptible to sweat stains.
Biggest problem is how to describe them in non-offesnive terms! 
I’m wasn’t sure how they came to be called a ‘wife beater’. I was thinking maybe it came from the 1951 movie version of A Streetcar Named Desire but images online show Brando wearing an ordinary T-shirt with sleeves. So I looked it up and wiki has the quote below but is certainly not conclusive and other sources have earlier origins.
The “official” sartorial term for such things is the “A-shirt”. Analogous to “T-shirt”.
I was surprised, speaking to a Brooklynite, that we used different terms but both disparaged the same nationality.
Since the title is different than the first line, I’ll just add that wearing an undershirt under a polo is Just Plain Wrong.
As for the argument that it’ll absorb sweat, if it’s warm enough for a short sleeve polo, that extra layer is going to make you sweat more It’s like the old ethnic joke of what do you want to take with you on a walk across the desert & the one guy replies, “A car door because if it gets hot, I can roll down the window.”