You have an interesting point of view about the short stacks, but this point tells me that you lack a few key things about short stack play.
As you might know, in cash games, the blinds never increase. As you might know as well, in cash games you can buy in for any amount which is between two fixed amounts, set by the casino. However, in cash games the pots grow almost geometrically, so it's not very hard to go all-in by the river, if you really want it to. As an example, if you raise preflop to 3 BBs, you get a caller and on each street you bet the pot, after the river betting occurs, you would have invested 107 BBs from your stack into the pot.
The implications of what I said earlier are these: if you have a short stack (40 BBs), then, because the pot grows geometrically, it will be very easy to go all in. In the worse case you'll go all-in on the turn, because you have little money to play. This means that you are forced to play big hands, because you need to win now. There is even a known, mechanical strategy, called short stack strategy, designed to play if you have little money behind. Although it's mechanical and you cannot make big mistakes, it's not a huge money maker. The difference between high and low cards, difference known as the gap principle is huge. If you play speculative hands, you will not win enough to compensate for the frequent losses due to the fact that you missed.
If you buy full stack (100 BBs), you'll have more money to play, it will be harder to go all-in, so you don't need all the time to have big cards. You can also play speculative hands that can form a monster hand and win the opponent's entire stack. Here, you can risk 3 BBs here, 3 BBs there because, in the most cases you'll miss, you would have risked 3% of your stack. The gap between high and low cards is lower than in the short stack scenario. If you hit and stack off your 100BBs opponents, it's more than enough to show a profit.
If you buy deep stack (100+ BBs), then the game is much more skewed towards speculative hand play. The gap here is so low, that you will almost never see AA or KK going all-in post flop, unimproved. Because you have so much money behind, on the long term it pays off waiting for a big hand (full house or quads) and shipping the money into the middle.
As the stacks increase, you need to me more skilled at play to be profitable in the long run. Anybody can shove KK being short stacked, but not anybody can maneuver his 250 BBs opponent into shoving his full house into the hero's quads.
Let's compare this with your question.
Short stack syndrome - the extreme measures a short-stacked player will take to stay in the game.
Sure, they might seem extreme for you, but for him they aren't at all extreme. He is forced to play big cards, he has little money behind, why shouldn't he be aggressive and try to get all-in as fast as he can. Don't you do the same thing when you have AA and you're in a weak game, with 100BB or less behind?
constant raises or all-in's most hands and as most of them have suffered earlier on in the game at some point (either by being donked out or by making a big mistake themselves) they're completely on tilt and behaving irrationally
Again, this is only your perception, as a good short stacker doesn't have a real reason to tilt. He's playing like this, again, because he has high cards and little money behind.
How to deal with it? You quite cannot. The main reason is that, if he will play big cards and you will be playing for his stack, not yours, you'll also be forced to take a stand with big cards also, cards that will mostly form TPGK+ or overpairs. You cannot call anymore with a low pair, hoping to set mine, because you don't have implied odds. The only thing you can do is to study the particular opponent and see his opening range, his shoving range, etc. and then construct your own ranges so as you will profit in the long run.
I hope it helped!
PS: the so called syndrome is no syndrome at all. It's simple short stack play.