I'd never really thought of... well anything you pointed out. If you would take the time to elaborate a bit more on some of your points, I (and likely others) could gain a great deal from your opinion.
I assume you wanted me to talk about more situations you could do with 3 moves I love? Here goes
Down throw - as wad pointed out, tech chases = :-) Some chars with those stupid 2nd jumps that can be cancled can be upsmashed out of d throw at certain percents, and some mid level fallers like marth can be d throwed to arialed sometimes. I guess that really doesn't sound like much for what I can come up for off the top of my head, but I guess its a throw and I shouldn't have expected pages. I will agree with axe that its prolly the worst throw, but its not bad IMHO.
fair - love me some fair. Now like axe said, not many true comboes involve fair, but some untrue comboes can happen with it 99 percent of the time. I watch alot of chad vids where he will do fair, land behind, and dsmash, it works pretty solidly. Then there is the fair>uair on gannon n64 talked about a while ago.
I feel fair is just a safe move if spaced well. I have played alot of good players in tourney, matt & tom r, dmac, viperboy, etc. I have never once gotten punished for spacing a fair to land way behind them. It doesn't always shield poke, but when good kids **** me up, its almost never after a fair.
Another thing I like to do with fair is to fair > grab. I love ledge hoping, fair, grab, b throw, edgegaurd. I love it so much that it has become a habit, and kids who play me alot know its coming, and I know its coming, but I can't stop. but if you l cancle your fair, you will most likely grab them.
However, fair to jab is a true comboe, and I loves it. Against walls and in pikas death pit in mountain phase on poke stadium, I will approach with fair, whether it pokes or not is irrelevent, cause I'ma jab right after like 100 times, and they can't stop it.
And another use off the top of my head, edgegaurding. If someone is far enough away where sweet spot is as far as they can get, and theres no time to spike/you don't wanna risk it, I find myself fairing falcos once in a while and taking a stock that way. Also, sometimes if I mess up my spacing on my ftilt, I will trade, and they will recover as I am falling back down and I don't have time to set up, so I'll just fair the edge so they go back down again.
Now in teams, fair is also kinda nice. your teamate gettin comboed out of a throw, fair, your teamate to far away to recover, fair to give them their up b back, your puff just rested some ho and you don't have time to jab, fair.
Bair - zig has a thing written out called like the reasons he loves bair or something, and I wish I could memorize it. But basically bair makes you look like you are in one place and your in another. Bair is also kinda hard to shield grab right away, its like a crouching puff. bair is a nice option right out of a rising uair. Bair is a pretty good finisher over all.
Man after thinking about it, bair is pretty situational and can be replaced by nair in alot of ways. Cause bair doesn't really combo INTO much, has about the same knock back as things, and IF someone knows the matchup they will learn how to punish a bair really good and won't shield grab it. And bair lasts so long if you wanna bair off stage, so nair easily takes that place.
I will say I stand corrected on bair, and kinda dthrow, but I still love fair