sharp corners and toddler noggins  

CONGRATS!!
We have a 6-month old and as I contemplate putting in 24"x24" porcelain tile floors I feel "your" pain. I cringe as I envision our daughter learning to walk and falling on that floor. I too consider the "intersection" of modern design and soft baby skin and am left wondering what to do, especially in light of our massive CONCRETE HEARTH! I guess, at the end of the day, I've resolved myself to thinking that I can't live in fear that the WORST is GUARANTEED. If you DO go with a Saarinen coffee table, might I steer you away from the MARBLE TOP.
Kids, so far, the BEST THING and WORST THING, all at THE SAME TIME!

Babyproof it.
Don't throw the bench out with the bathwater. Some styrofoam packing corners from U-haul should do the trick.

Generations of children
have been raised in homes with normal furniture, and no one has thought it dangerous until now. I don't understand it, I'm sorry to say. Are today's parents thinking of abandoning the care of their offspring, letting them "free-range" without supervision for minutes or hours at a time ? Or perhaps they don't trust the inlaws, the babysitter, or the spouse to take the same care that they do ?
Adults can feel the difference underfoot between a wood floor (in a wood-framed house) and a concrete slab. An infant or a toddler is so much lighter in weight that the difference is literally nil. Kids fall -- it doesn't kill them, and they learn something each time, getting better rapidly at negotiating their surroundings. A scratch or a scrape is the price, soon forgotten (but not the lesson, hopefully) and quickly healed. To deny growing children the normal environmental interactions can (it seems to me) delay the necessary learning process.
Of course, we fence stairs and pools -- there's no need to invite disaster. But if every right angle corner in the house is seen as a hazard, where does it stop ? Knife-edges, maybe, but not the corners of a Nelson bench -- which in any event is light enough to slide when struck, greatly reducing the force of impact. (If Grandma is sitting on the bench, thus preventing it from moving, then she would presumably be watching the little one at the same time -- no ?)
Where did the current over-protectiveness come from ? I can't say --but can offer one observation: once a caution is suggested, it is hard to ignore it -- one seems shamefully careless or. . .ignorant. So the list of "accepted cautions" grows, and grows, all because no one dares say "enough." More and more of life's little inconveniences are turned into "medical issues" (thanks to Big Pharma) and remedies are sold. Let's not let the fear-mongers turn our lives into self-perpetuating prisons. Remind Grandma that she was a little girl once, and she turned out fine. She, and you, aren't being "neglectful" when you raise a child in a normal home -- rather than a padded cell.

Not necessarily...
Nolan busted his mouth on our Bertoia bench. But he could've just as easily split his head open on anything else, just as Liam did on our driveway. It's going to happen. If getting rid of acute corners makes you feel better, do it. But you could also move the platform bench into a side room. Very versatile piece.

I should also mention...
that coffee tables are completely pointless with toddlers around...

Perspective
Congrats on the new addition to your family.
We have managed to keep our son alive to the ripe old age of five without making any alterations to our environment or furnishings. I know how freaky it is when you have a tiny newborn, but trust me, they are much more resilient than you think. We did not do the safety latches on the cabinets, or even the electric plug covers. We meant to, or kept an eye on his behavior with the thought that we could add these precautions. But they never proved necessary. And our guy is very rambunctious, inquisitive and high-energy.
He did take a spill once and hit his face yielding a nice little cut (right at the corner of his eye) on the shell of the Eames lounge chair ottoman. Something that is all rounded edges. Go figure. His first stitches came after an encounter with the edge of a table while at preschool. He has a very dashing scar in the middle of his right eyebrow. Five stitches, but he survived, and he'll be the first to tell you... chicks dig scars.
Not to make light of it, but people worry about too much in my opinion and you can't control everything. I know most of my childhood injuries came from my own recklessness and wild energy. So I say don't sweat it too much. Don't leave piles of straight razors lying about, but don't worry too much about furniture with right angles. Like your aunt said, even round tables are a hazard, so what are you to do? Unless you want to live in a combination Aarnio/ Platner environment there are going to be hazards. I've also found that living with and growing up with this furniture (dangerous and/ or expensive) makes them and you comfortable around it. Besides, who wants to live in the equivalent of a padded cell?

Reupholster your furniture with stuffed animals.
Sure, it SOUNDS crazy...
http://gizmodo.com/380128/75000-chair-is-made-of-pandas-pandas

SDR...
Once again, I am in agreement.
US culture (and perhaps all "developed" nations?) has gotten so baby- and kid-centric, it has gone far beyond ridiculous. The amount of waste being generated due to this mentality alone is truly mind-boggling.
whitespike, I do congratulate you and wish you all the best. I just hope that modern and child can co-exist for you, as I believe that was one of the intents of modern design to begin with.

What a cutie!
The current hysteria over babyproofing is a result of manufacturers realizing there is a market for this stuff and convincing the public that it's necessary. Couples are waiting until later to have kids so they have more money and are more willing to spend it on babyproofing products.
Don't worry about your bench. Get a gate for stairs and get some latches for kitchen and bathroom cabinets. Put breakables up high. Don't have dangling power cords. Get those handy outlet things where you have to slide the cover sideways about 1/4" to get the plug in. All the rest is superfluous.
A lot depends on the kid, too. Some hurtle through space without a lot of control over their movements. Others are very cautious and careful. My grandson is the latter type; he will be one year old tomorrow and he can climb up on chairs and sofas and sit nicely, and back himself down onto the floor again with great control. He's been walking holding onto furniture since 7 months old and only just started walking unsupported, we think because of his cautious nature. All I can say is, YAY.
Good luck and don't worry too much!

Maybe
what's a safe and comfortable environment for kids -- is the best thing for grown-ups, too ? It's never too late to upgrade the home front !
As I forgot to say, Congratulations Mr and Mrs Whitespike. Live long and prosper. . .!

...
The only thing I could add would be perhaps to focus on getting some rest right now rather than worrying about your furniture.

If all else fails...
You can always paint your house entirely white and photoshop out every single piece of furniture, save a purple beanbag chair.

Dearest Whitespike's et al..w...
Dearest Whitespike's et al..what a sweet little lump! Cute as a button. Being childless myself, when the little tykes come to visit, I tend worry more about what might happen to my furniture than anything...in the event of an accident. Children with scars and scabs can look charming. A chunk missing out of my Nelson bench would be a damn shame.
Congrats!

Timely thread
My wife and I are expecting our first in October and both of us have been eying the Nelson bench. We decided to move it up in our bedroom. I feel like there is only so much I can do...anything HARD is going to crack a noggin...there's no way around it.
Like others have said, I'm going to worry more about chemicals stored under the sink, a stair gate, and electrical appliance cords. And getting sleep...'cause I know my days of 6-hours of uninterrupted sleep are going to be over soon. :/
fm