The analogy is really far from the point. Sorcerers are not restricted in spell schools wrt wizards. Neither are Warlocks, bards, druids or clerics.
Sure, there are some individual spells that are in a school but that a caster cannot take, yet they aren't barred from all spells of that school.
This instead is exactly what happens with combat traditions.
The restriction is also cheesable by dipping 1 level in fighter: once i take 1 level in fighter, I should have access to all maneuvers. Maybe I cannot take all maneuvers from all traditions (there's no mention about this yet in the disclosed material), but surely at least for that level you have full flexibility.
Regarding the fighter, for what I read in the preview material and comparing it to the other classes in the preview and the adept just posted, it feels really subpar. It doesn't feel an unparalleled master of any weapon, because there's no particular features that directly improve weapon use. It doesn't have the same staying power of a barbarian (rage, hit points) or probably even a paladin (spells and lay on hands). It just has a few more maneuvers, but curiously less effort than an equal level adept. The adept itself can get level 5 traditions, and I bet the same will happen with the barbarian and the paladin, so we cannot even say that he is the only one able to pull off those high level stunts.
What is the shtick of the fighter, then?
I agree that traditions as written have a link with the base class, but this clashes with the reasoning behind calling the paladin a "herald", or the monk "an adept": it forces a description. Tarzan could well be an adept with maneuvers from Tooth and Claw tradition, more than a barbarian.
Okay, there's a bit to unpack here, because you're asking questions on several fronts, so bear with me for another longer post.
I'm going to be somewhat vague here so as to avoid derailing further previews that the boss has planned, but I think I can speak in general terms without stealing too much thunder.
First, the analogy actually works better than you think it does. Your assertion seems to be that a cleric gets Abjuration, Conjuration, Divination, Enchantment, Evocation, Illusion, Necromancy, and Transmutation (the "classical" schools of magic) spells even if they're not the
same ones as a wizard, and the combat schools, in this line of thinking, are equivalent to the classical spell schools. That's not how they were designed. The "classical school" equivalents of maneuvers would be things like "damaging strike, defensive maneuver, evasive maneuver, hampering strike, etc." Think more along the lines of the types of roles you see represented by a spellcaster: Manipulation and trickery for a bard, healing and support for a cleric, battlefield control and blasting for a druid, etc. (By the way, those previously "implied" magic schools are also more explicit now in A5E. In addition to Abjuration, Conjuration, etc. spells are also tagged with things like Nature, Affliction, Communication, and so on, and the team has used those tags in design, but you'll have to ask Morrus if you want more specific details.) The combat schools all have offensive abilities, those that mess with opponents in some way, etc. But the flavor is closer to those new schools like Nature, Affliction, and Communication than Abjuration, Conjuration, Divination, etc.
Before I continue, it's also worth noting that if you compare the class tables for the fighter (which you can see in the post
here) with the adept one (which is
here) you will notice that the fighter gets more than
double the number of maneuvers an adept gets, topping out at 17 to the adept's 8. Fighters start out with 3 maneuvers at level 1, and get additional ones at levels 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, and 20 whereas an adept doesn't get maneuvers at level one, pick up their first pair at level 2, and then gets additional ones at levels 4, 7, 10, 13, 16, and 19. By the way, heralds and rogues get maneuvers at about the same rate as the adept and marshals, rangers, and berserkers have more than the adept but less than the fighter. So the adept is essentially a "tertiary" maneuver user like an Eldritch knight or Arcane trickster was a tertiary spellcaster in O5E. The berserker is analogous to one of the secondary casters from O5E like paladin or artificer.
So in a very real sense, you are kind of asking the same thing as "aside from being good at magic, what makes a wizard special?" And like with the wizard, there
are some other neat features, but they all tie back into the central focus of the class, which with wizard is "casting and knowing spells" and for the fighter is "person who is hyper-specialized in combat." The first thing I am going to point you to is the fighting style feature that you may have skimmed over. The ranger and herald classes now no longer get access to that feature like they had in O5E (and as I'm sure you know, the O5E monk and barbarian never had access to it in the first place), so that's a further point of being better at fighting than their less-focused peers. But not only is that feature unique to fighters now, fighters now have twice as many choices for that feature as the O5E fighter did, and a couple of them let them do things with maneuvers that no other class can. As you move up into higher levels on the table, note the multiple instances of Maneuver Specialization. Again, I'm not going to get into specifics right now, but there's clearly something going on there that represents a higher-than-normal level of skill with maneuvers than the other martial classes get. And in addition, a lot of the fighter's exploration and social pillar abilities are really strongly flavored toward a truly masterful warrior. Think about some of the stuff that character type can do in media: they're good at menacing people with a glance, sizing up threats, staying on alert for long periods of time (google the "cooper color code" if you're not familiar with that real-world military/law enforcement guide to different levels of situational awareness) and so on. Indomitable now also has two additional use options in addition to the one it had in O5E and those are pretty cool. They're both the sort of thing that you will get
plenty of opportunities to use, as well, not some kind of highly-situational thing.
If what you want to play is a "pure" warrior like a Spartan, samurai, the archetypal non-holy knight, a Welsh longbowman, or a Roman legionary or gladiator, you really do want to build them as a fighter. Every tiny aspect, every exploration knack, every social pillar ability feeds back into the concept of someone who has absolutely
mastered the art of pure combat skill. I
really wish I could be more specific, but I'll say this in summation and for emphasis: don't assume that new abilities do nothing, and don't assume that abilities that overlap with the O5E fighter only do what they used to do. As I was composing this reply, I sat here with the O5E SRD open in one tab and the new A5E fighter rules open in another so I could compare. It is
quite an upgrade.