Personally, I don't think so. Besides, do what you like. I have a Toto Legato sink (square with a trapezoidal basin) and Jado wallmounted faucets. I love the look and get tons of compliments on it.

I hope not, we will have one installed in a couple of weeks. Ours is Toto but smaller than the Legato because our countertop isn't very deep but think we will be pleased.
One thing I paid attention to was the numerous comments/complaints about a sink that has a flat bottom. Seems that water puddles in these after use and some found it necessary to wipe the sink after every use because of th puddles. There were enough comments about this that I purchased one that wasn't flat bottomed (though I liked that look). Good luck.

It probably will look dated. But who cares? Do you like it? That's what matters.

I have flat-sinks in my master bath (Kohler verticyls). I was concerned about the drainage too but it has not been an issue at all. We never have to wipe out the sink after use.

They may look vintage rather than dated :)

There's always a period of dated before anything reaches vintage status. :)

Considering we went with a square sink for the first house we built nearly 30 years ago... and are considering them again...don't think it will be anymore dated than all the other finishings/furniture you will choose in your bathroom! LOL Now if you chose it in purple...

I just put three of them in - Kohler Ladena - beautiful! Anything will look dated depending on new products that come out but I think sink shapes will stand the test of time better than some tile designs, lighting fixtures and such.