I don't buy this dichotomy you're setting up.
Well, as I have already said, it's not absolute, but then very little is. But it is noticeable -
vide the number of debates it brings about.
There are ample elements of skill involved in SoD situations;
OK, let's break them down, shall we?
designing characters with good save bonuses and other defenses,
Before 3.x this simply amounts to choosing a class. IIRC Clerics had the best save vs. death - so presumably an all-cleric party was expected?? In the later editions you had more scope to "build" for defences - but with three saves/NADs plus AC to cover you had to nerf other areas quite badly to get good in them all (although one of the PCs in the 4E game I run has been built this way).
Again, prior to 3.x the rule for surprise was "the party is surprised on a 1 or 2". How do you avoid that? Well, of course, there is a way, and IME it was actually quite common, but I'll come back to that.
and anticipating encounters,
In the "regular" dungeon this was only really possible with magic - and then only to the extent the DM wanted to let it be (part of the wider point I'll make later).
Yep, good old "old school" play - "memorise the MM or you're toast". Some folks like it - good on 'em.
countering it in various ways.
Right - this gets to the widest argument I have here. How do you avoid surprise, anticipate encounters or counter dangerous/SoD abilities when no edition has had actual explicit rules for doing any of this? Easy - you play "blag the DM". More formally, you invite the DM to use their power to improvise additional rules on the spot to allow the regular rule (if any) to be bypassed or to allow priviledges of information or exemption from power effects that are not a part of the normal rules. If you can get the DM to like what you are proposing - because it fits their conception of what is "realistic" or it fits their conception of what is "cool" or it fits some other criteria they have for what they want included in the game - you get to play by new and different rules. If you can't persuade the DM to like what you propose, you're SOL.
"But, this is a game of skill!" you might say. Sure it is - but (a) it's not part of the game as written, really, just a surrogate game that many found to play instead in the early days, and (b) it's a game that's so old and tired that, despite enjoying it for a few years when it was new, I really gave up on some time around 1981.
The roll itself is chance, but the application of the ability is hardly "pure chance".
True - you can use your "Blag the DM" skill to see if you can get the base rules changed (see above).
Conversely, essentially any D&D battle involves numerous dice rolls. Typically their results will be "average", but it is entirely possible for a battle involving only attack rolls and hp to be decided by luck, and many such battles do not involve a whole lot of skill.
If you have few hit points you need to be extremely careful, if you have lots you can be a bit more adventurous; there's the most basic application of skill right there. The point is that there are things that are written into the game that you can do to mitigate the risk. Absent significant DM license, with SoD there seldom is. Another comment was made about "starting out of range of the SoD effect"; with line of sight effects or in a "dungeon" that's usually not a real option.
Also, if you're not into games of luck (which is fine; I'm not big into emphasizing that element either), you must really hate rolling for ability scores. Is that "bad design" as far as D&D is concerned?
Look again; I didn't say that any randomisation is bad - just that which creates a "you lost" situation with no opportunity to avoid it (in play). Characteristic generation is different; it sets up the resources that you will have to work with in play, but it doesn't lead to "you're dead" (except, maybe, in Traveller!). That said, I do prefer point buy for D&D, but I wouldn't refuse to play just because it was a "roll stats" game. And HârnMaster games are positively enhanced by attribute rolling (because the aim of play is very different).