Maybe I'm playing imagining the wrong game, but this would not be one of my assumptions when creating a Solar and it would not be one of my assumptions if I headed a team tasked with writing a new edition of Exalted. A newly-Exalted Solar might be powerful, absolutely, but they should not be immune to the Wyld Hunt, even if they're a Dawn.
I feel like the idea that starting Solars should be on equal footing with high-essence foes leads to the idea that Solars are the Protagonists of the setting and everybody else are NPCs. Why play anybody else if a Solar can come in and take a Glorious Solar Shit on everything you've done without a meaningful countermeasure? How can anybody else matter if Solars are just that damn powerful from the jump?
I'm sorry, but this is just a somewhat incomprehensible take to me? Yes, a newly-Exalted Solar shouldn't be immune to the Wyld Hunt. Neither should Ma-Ha-Suchi or Ahlat (or rather, the reason they should not be concerned about getting Wyld Hunted should have more to do with boring questions of supply lines, logistics and the Wyld Hunt's need to bring supporting troops into enemy territory if they want to mount a successful attack on a very distant and inconvenient location such as the Nameless Lair rather than their ability to personally solo a Wyld Hunt's worth of Dragon-Blooded).
The rest of your post makes even less sense to me! A good 80% of those freshly-Exalted Solars will be noodly-armed Twilights, scheming Eclipses, larcenous Nights and oratorially-inclined Zeniths - not exactly the sort of people you have to be concerned about, if your main issue is "they will personally waltz into my throne room and bash my face in". (Admittedly, if you have been steadily building up your vast empire of crime, the emergence of Solar Sherlock Holmes in your area
should be a concern, but even that shouldn't just be a case of "he glances vaguely in your direction and all your schemes come unraveled".)
Of the remaining 30 Dawns, you can expect a grand total of 6 being active in your whole Direction at once, at any given time. Or, more realistically, around 3, if we count the eight directions as separate and maintain a reasonable buffer for the vague category of "currently unattached to a host, in other realms of existence, out of commission for esoteric reasons, or living incognito on the Blessed Isle". Of those 3, maybe one will actually have the capability to personally come in and ruin your day - it is eminently possible for a Dawn to be practically impossible to kill but no more of a threat than a Dragon-Blood offensively speaking, very swift or perceptive but roughly on par with a reasonably experienced Celestial otherwise, or just... currently not much of a fighter (watch out for them in two years though!). So, a realistic answer to the question of "why would I play anybody else if a Solar can just come in and take my lunch" is "a Solar is not going to come in and take your lunch, because your whole entire Direction has one Solar who could even have a realistic chance of doing that in the first place, and they're probably otherwise occupied".
I also take umbrage with the implication that just because a chargen Solar could, theoretically, waltz up to Ahlat or Ma-Ha-Suchi and beat them to death (maybe, with some luck), that automatically means everything you've ever built will necessarily be burnt down and the earth salted the moment said Solar shows up on your doorstep. Do you have no allies? No underlings? No army, no infrastructure, no favors to call in, no treasury to draw upon for some earth-shakingly powerful Artifact that could tilt the balance in your favor, nothing? Just because the Dawn can take on Ahlat in a white room (maybe, if they have a good build and get lucky with their dice rolls) doesn't mean they can also solo Ahlat, his brides, and his whole entire spirit court all at once. It just means that if an entire circle of PCs puts their mind to it and scheme, beg, cajole, sabotage and do everything else in their power to undermine his alliances over the course of a whole entire story arc, and
then manage to deliver the Dawn to his throne room uninjured and with a full mote pool, they have a better than even chance of getting out of there victoriously. I think that's a perfectly valid and appropriate goal for the first major story arc of a campaign. Others may disagree! I wouldn't even be mad if a new edition of the game dropped and said "yeah we're envisioning this sort of story arc as more of a... mid-point for a chronicle kind of thing"!
Lastly, I think Exalted is just... not the sort of game where your ability to bash someone's face in is really supposed to matter all that much in the grand scheme of things? I think the game line has very consistently been communicating, for decades, that its idea of challenge is not meant to come from "can I do the thing?", but rather "can I do the thing and cope with all the unintended consequences that fall on my head in the aftermath?". Like, yeah, cool, you've beaten the shit out of Ahlat and maybe even got your party's Twilight to deliver the killing blow so he won't even regenerate. Congratulations, you now control Harborhead. What does everybody else think about this? How does the Realm feel about losing a big and important Cathak-controlled satrapy right as they are on the cusp of civil war? How does this play with House Cathak's position of "teehee we will just support whoever seems like the best candidate for the throne" - will they feel like they can afford to dispatch a major force to deal with your burgeoning empire? Will other Houses feel like going "oh hi, we'd sure be happy to help you with this unfortunate Harborhead situation if only we were on the throne" will help them curry favor? What do Ahlat's godly allies and friends think about the fact that you guys have just gone and forever-murdered someone they've had some sort of a relationship with for millennia? What do the people of Harborhead think about you guys doing that to the god whose worship has been, like, a major cultural and religious anchor for the entire region? What's going to happen to the whole cattle-raiding thing now that "war" and "cattle" are no longer necessarily intertwined under the auspices of the South's directional god of war? Speaking of which, who are going to make a play for trying to become the new Southern God of War now? What will that look like? Will it involve your new empire? How?
I think those are the sort of questions Exalted is more interested in posing after the PCs throw a giant monkey wrench into the whole lovingly-built little Rube Goldberg machine of politics and mayhem that is any even half-decently written Exalted location, and in order for those questions to be posed, it is fundamentally
necessary that the PCs be able to effect that kind of change.
But that's, just, like, my opinion, man.
