Hi! I work as a visual and UX designer, please let me contribute with my point of view.
I think the way the question was formulated is pretty biased.
Flat design is a trend, as thin fonts right now, or just as any other trend (remember “Web 2.0 glossy buttons”), you can follow a trend and be unique, just don’t copy others.
As a trend, it can be emotion-less or not. What makes a design cozy? That’s a challenge for the designer to play with.
When you say “it feels cold/unwelcoming/barebones for some” I think you are expressing an opinion. A client recenly asked me to change their whole site to “flat” because the current one looked to “heavy”. That’s the way trends affect people.
Opinion is subjective and not so good for user experience. The real factual disadvantage of flat design is that it loses visual hierarchy: users sometimes don’t know what is clickable and what not, because a button ends up being just a colored square.
But that’s not even a problem of flat design, it was a problem of Windows Metro UI mostly (Windows 8), that went too far.
In art, all trends tend to go to far, and then step back a little, if they are real trends. Flat is a real trend, glossy buttons not so much. What makes flat a trend is that it has a backing philosophy: content first.
So, flat was good in introducing that concept. That’s it’s contribution to the design world.
In order to have an updated look, you have to follow trends a little.
I would go with something more modern, cleaner, but not-so-flat. I like to have some volume in my buttons.
Current design looks a little old, I have to say, that’s just the way things are in this crazy web era, 2 years old is old. 4 years is ancient history.
I think the problem with the current design is not cleanliness, it’s that it should be more solid, consistent, and that should be achieved with consistent margins, paddings, font sizes, borders. Bootstrap will provide a better foundation for that.
I think the next challenge will be to come up with a design that looks more modern, but unique, rock-solid and appealing to new users. Any designer can log in into the site and immediately notice that it needs a more solid visual language. I think that’s the next challenge, flat or not.