The solution is pretty cheap.
There has been a massive price drop on 22" widescreen LCDs that are a few pixels shy of 1920x1080 with DVI inputs. The AppleTV is a dirt cheap media server. Sounds like a no brainer to me for someone who isnt pinching pennies and does not like spending their weekends trying to burn a bunch of DVDR's.
Not only that, but there are a lot of educational podcasts available (including some very impressive HD shows, like DiveHD) that my daughter just loves.
The AppleTV remote (which i have a pile of now, as they come with each of these macbooks) is pretty much kid proof. I have a 3 1/2 year old who cant really read that does just fine in the menu. Its all image based anyway.
Forget the 160GB model...just stream everything. The thing with the AppleTV is once you delete those movies off your local hard drive, they go away on the AppleTV. Might as well just mount a big file server and call it good.
Pairing it with an LCD computer monitor instead of an HDTV at about $300 with the Apple TV at $300, I would call a cheap a solution for an adult's, say, den or home office. $600 for a TV/DVD in a child's room is not what I'd characterize as cheap, pinching pennies or not. There's also no DVI output on the Apple TV -- component and HDMI only, plus RCA composite and optical audio -- so you'd require some sort of HDMI-to-DVI adapter. And you'd need at the least powered speakers or some sort of stereo system for the audio. You're pushing $800 at least. (And that system won't be able to play TV at all if you do now, or wish at a future date for the kids to have broadcast or cable/satellite TV in their room. For that price, you may as well get your kids a full blown 17" iMac, which can play all media, DVDs, etc., and be their computer when they're older.) A standard-def TV with built-in DVD player for a child's room is about $150. In your case, it's nothing, as it already sounds like you have the necessities to play DVDs in your kids' room.
It's only a time savings if you're going to buy all your media from the iTunes Store. There's a lot of Disney/Pixar and a fair amount of Disney stuff on there, but you'll be locked to an Apple TV -- no taking it with you to friends or relatives houses -- and there are other kids' movies from studios other than Disney. If you buy physical DVDs, you're still going to have to rip them to get them onto the Apple TV as the ATV won't play DVDs. So the time investment is still there, which is mostly unattended. Burning the duplicate DVDs from blanks, the ones that won't cost you $10-20 to replace if they get scratched beyond repair, will only take, with something like Burn, about another half hour or hour -- there's encode to MPEG2, the DVD encoding format involved -- but that's all unattended.
He is however right about skipping the 160GB Apple TV model. If you're not keeping the movies in your iTunes library, they don't stay on the Apple TV, so it's not like that extra space on the ATV frees up space on your Mac. I just archive things I'm not watching on my Apple TV to a external hard drive that I also use for back-up, and then copy them back to my iTunes library when I want them on my iPod or Apple TV. That takes a few minutes. It's the sync'ing them to the Apple TV over Airport that takes forever. As for the video podcasts, if you find any of them of value, these aren't copy-protected media and you can burn them to writable or re-writable DVDS with burn, too. They won't be in high definition, but high-definition barely matters on a 17" or 19" TV set. I would bet high definition barely matters to a young child, period.
He's also right about the remotes. They're so simple, they'd require a focused effort to break. Also, he's more or less right about the interface. Picking music would be difficult for a child who can't read, but learning the steps to play a video by watching you do it -- depending on the child and how he learns processes -- they'd probably pick up in a few days.
Obviously, it's up to you, but I think spending near a $1,000, minimum, by the time it's all said and done, to prevent your kids scratching DVDs is too much when you can do it for about $20 with the equipment you already have. Also, for me, the ultimate goal is to teach my sons to treat the DVDs well, because this is going to apply to CDs, which of course you can duplicate, but also to console video games in the future -- and those are now $50 or $60, and you can't duplicate back-up copies of those. I think, too, slowly teaching them to treat valuable collections well, like DVDs, will apply to some degree to treating all of their and your things well in the future, when they have the physical coordination to handle things with care.
Realize, I did strongly consider the Apple TV for my sons' room, too, along with buying a new HDTV to go along with it. But ultimately I decided it was a gadget-obsessed way to push in a thumb tack with a jackhammer.