I drool over the NSX, though I fear my expectations would be too high. That said, I still consider buying one, but not as my only car.
Baby on the way? I'd be getting a WRX hatch instead for the same BRZ coin. A bunch of power and practicality. I have a 4yr old - he climbs in the back of my BRZ fine, but I wouldn't want to use that car for hauling a newborn. (Plus when my son was a newborn, my wife would ride in back with him - can't do that in the BRZ!)
I'm in a somewhat unique position of owning multiple cars. You say you didn't like the soft top of the S2K, but they sell hard tops. You could get a Miata (first gen) for cheap that is well kept and has a hard top. You can modify it for cheap money too - quality mods don't cost a fortune on those cars.
The BRZ... what to say? It's a great car. It's bigger than my first gen Miata. Ride is great, more power, nicer interior, more comfortable, more room. Handles great - differently than my NA, as the Miata is 500 pounds lighter and smaller, you can just dance around in that car! But the ride is more jarring. The BRZ goes where you think - almost telepathically. You move the steering wheel and the car turns - right where you expect it to. Very easy to throw around as well - like a bigger Miata, with some serious chassis rigidity!
Now I love my Miata, but the BRZ does 9 things out of 10 better. Oddly, I enjoy the Miata a little more bc there's more "connection" and "rawness" there. Less isolation. Both cars put a smile on my face.
That said, since I have the BRZ, I could sell the Miata and replace it with an NSX (ok, there's a huge price difference but lets look past that for a minute). The NSX would be my sexy exotic. Would I drive it every day? No. But 3-4x per week maybe. Or save it for a treat, or when work is stressful and I need a pick me up. It would just be awesome to park in my garage. But... the BRZ would be more practical, more space, more comfortable. Less sacrifice. Still allow my son to ride with me. If I had both in my garage, I'd drive the NSX once a week just to feel "badazz", but drive the BRZ daily.
Now I'll toss back in the WRX/kid comment - bc I own a WRX wagon (Cobb tuned and modified). Holds a ton of stuff, extremely practical. You don't realize how many thing a 6 pound baby needs that comes in large boxes! And it's not just practical, but also quick when the turbo kicks in. And the AWD is jaw dropping if you've never driven AWD in the rain. You're at a T intersection trying to turn on to a main road, and there's 100% traction. The car just moves like there's no water on the road. And when you toss it around in the wet, you get these 4 wheel drifts instead of understeer or oversteer. Can be a lot of fun while being super practical. Not so great on gas though, but better than an SUV.
So - what should YOU do? If you're bored with the NSX, sell it. Buy the BRZ. Or better yet, buy a WRX hatch and also a first gen Miata to throw around curves. In either case you're going from "cool exotic car driver" to "general public" - but at least not all the way down to "Camry or Prius owner".
I think you'd like the BRZ, but it would never be as cool as the NSX. You could always tell people you used to drive an NSX...
(And depending on how you are, when that baby comes, "car coolness" might be the last thing you care about, and "car safety" could be the only thing that matters. Those little ones are so tiny and delicate at that early age. Sure, later on they become indestructible, but the first couple years you just want to cradle them from any harm.)