Removing mysticism doesn't make mages any weaker, because most of the spells in mysticism are placed into other schools, rather than removed entirely. Removing skills only makes certain character types weaker as long as they still can do what those skills allowed them to do, in some cases it can mean it makes them stronger, as if those mechanics initially governed by a removed skill are moved into a different skill, that skill may end up effecting more things, thereby making it strong, in theory anyway, in practice, there are a lot of factors which decide how powerful a specific skill is, some skills that are fairly specialized can still be quite useful if the task they govern is something that is very beneficial to the player and can't be performed by other, more versatile skills. Likewise, removing intelligence doesn't make mages weaker, as you can still raise your magicka, you just increase it directly upon leveling up rather than having it calculated based on intelligence. And willpower... we don't know about that yet, as the main thing willpower did in Oblivion was control your magicka regeneration, and we don't know how that's handled in Skyrim, though if magicka still generates in real time as in Oblivion, and due to the absence of willpower, is locked at a specific amount, then it will most likely be a moderate amount, lower than what you'd get in Oblivion with a high willpower value but not as low as a low willpower character, assuming that the balance here is still basically the same as Oblivion, which it is entirely possible that it is not. But what's ultimately going to decide how powerful mages are is not what skills and attributes exist for them, but what they can actually do and how well they can do it in comparison to other classes, and really, I'd argue that the latter is more important than the former, it's not going to matter if mages have access to a spell for everything you could possibly think of that could be accomplished with a spell if none of these spells actually do it well. Even if Skyrim's mages turn out to be less versatile than Oblivion's, that doesn't necessarily mean they'll be less powerful, I'll have to judge whether they are or not after playing the game. Though it does look like battlemages may suffer due to the mechanic changes of Skyrim, as the only way to have a spell and a weapon equipped at he same time is to have one of these in each hand, meaning they must sacrifice both the ability to have one spell in each hand and the option to dual wield, use a shield or carry a two handed weapon, which might actually be a good thing as battlemages could be a little overpowered in past games. In theory, as I see it, a battlemage is supposed to be some who can both use magic and fight in melee, thereby sacrificing a degree of effectiveness in both tasks, essentially, it's a tradeoff between having a wide variety of talents that you can perform decently, or a narrow variety of things that you're very good at. This could also increase the desirability of pure mages indirectly by making it so if players want to use magic, some options will only be available if they're willing to not have a melee weapon equipped at the same time, though this only applies if the advantages gained from doing so are significant enough to be worth not using a melee weapon.
And I wouldn't necessarily say mages were weaker in Oblivion than in Morrowind either, sure, they lost a few spells, though the only removed spells I actually used often were levitation and teleportation spells anyway, and the former was actually essential for completing the main quest, whereas the latter's main use in a game with map based fast travel would be to escape from battle anyway, and if you need to do that, it means you're already losing. On the other hand, they gained several advantages over Morrowind mages, such as magicka that regenerates over time (One of the most frustrating things about playing a mage in Morrowind was the fact that you never seemed to have enough magicka, aside from the fact that if you don't add racial or birthsign bonuses to your magicka, or fortify intelligence, the maximum amount you could achieve was really quite pathetic, there's also the fact that once you run out of magicka, the only way to replenish it is using potions, which add extra weight, and that is a bit of a problem if you've been adhering to the usual stereotype of frail mages who would fall over if you just lightly tapped them with a finger, and resting, which is not always an option, and in any case, sleeping for hours on end after every single fight isn't really beneficial for role-playing.) not to mention spells always succeed, which admitably fits in with some of the other mechanics of Oblivion (If an attack connects, it always hits, for example.) but I've had a lot more frustrations caused by failing at spells than attacks missing, in part because spells cost magicka, sometimes a large amount, whereas attacks only drain fatigue, which regenerates quickly, and in part because I've had several experiences with dying in a situation where I should have been able to survive simply because a spell failed when the chance of success was quite within acceptable levels, simply because of a factor completely outside of my control, finally, mages could cast spells without needing to put away their weapons and "ready" the spell, making casting a spell much more streamlined, though admitably the ones who benefited most from this were battlemages and other characters who combined magic with other skill types rather than pure mages, but as I see it, magic in both Morrowind and Oblivion was most useful when used together with other skills and was not reliable as your only tool to ensure success anyway, and with the factors I mentioned, I'm not sure if they made mages more powerful, but I certainly feel like they removed some of the frustration of playing a mage, and really, the reason players usually strive to gain powerful things in games, aside from bragging rights, is to remove frustration anyway.
In OB, you had the choice, as a valid part of the game mechanics, to enchant to 100% chameleon, use items to give 100% resist weapons or reflect magic, and create massive damage through weakness stacking. In Morrowind, everyone knows the old fortify intelligence, fortify intelligence, fortify intelligence, do something else routine.
These are not cheats or exploits, these are part of the game mechanics, and to not use them, out of principle or need for challenge, is deliberately gimping your character below what the game allows.
I suppose you could argue that those things are part of the gameplay mechanics, but I hardly think that the option to completely strip any sense of challenge from the game is a necessary or desirable gameplay mechanic. You might as well just had an option to toggle off fun in the options menu, because that's essentially what using 100% chameleon amounts to.
And as you said yourself, choosing not to use those things is deliberately limiting your character even when the game allows you to be stronger, which I think is another compelling reason to remove those abilities, making a fun game is supposed to be the developers' job, my role should just be to provide a source of income for the company that made it and enjoy the product I get in return, it shouldn't be my job to make the game fun on my own because the developers didn't do their job properly. The only reason we would need to intentionally limit ourselves to keep the game fun is because the developers did not do their job of balancing the game properly. Of course, I did, in fact, prevent myself from doing those things, but that's because I had to to keep the game fun, I can't say I'd miss 100% chameleon if it were made impossible in Skyrim (Though entirely removing chameleon to prevent it is like amputating an arm in response to a paper cut.)
Mind you, I agree that mages should be powerful, in fact, if we take out things like 100% chameleon, I'd argue they were quite overpowered, but power in a game needs to have reasonable limits, because in the end, games are created to be entertaining, while certainly having a high level of power can be quite entertaining, if it reaches the point where nothing at all in the game can challenge you, it often becomes boring. power is supposed to help you overcome obstacles, but that doesn't mean it should automatically eliminate them for you without any effort on the player's part.