Yes, but.
On a Doylist level, Anchors serve to make you go out and get to adventuring. On a Watsonian level, if invoking Ligier's name to get a fraction of his power can burn an city to radioactive ash, then he needs to be able to.
And if he can, then why is an Anchor required for your Enlightenment 10 Slayer to burn a city into radioactive dust? He's on the same level of enlightenment, he's got a hell of a lot of power himself. Why can't he?
Once again, you are ignoring the fact that the sorcerer is not a passive participant, and they are in fact pumping a huge number of motes into Total Annihilation. Your argument is as exactly as facile as saying that people should be able to spam canon!Total Annihilation just by building one's self into a rage and whispering the lost name of Ligier, because that's all the spell description text says the sorcerer needs to do (ignoring its 65m, 3wp cost).
You don't get to cry "Watsonian" when you're ignoring the in-setting logic in favour of your straw figure.
So, no, you are not just "invoking Ligier's name". You're tearing a hole in reality and drawing a fraction of the giant green sun that dwells at the heart of Malfeas through your magic. Or you're drawing on the tiny ember he granted you when you signed your pact with him, and feeding it vast amounts of fuel. Or perhaps the fact that the two of you hate the same person enough to be Allies means your natures are akin, and so letting your mutual hate flow into the essence makes it burn green.
As for why Ligier can burn cities-sized regions in Malfeas to slag when he focusses his wrath on them... that's because he's a giant sun as well as a man. Are you a giant burning green sun at the heart of the demon city? [1]
No. No, you are not. Just like Munaxes can make entire towns fall into her depths, because she's a giant chasm while Exalts are not.
Yes. Ligier can do things natively of a scale that Exalts have to use sorcery to achieve [2]. Exalts can do things Ligier cannot. This is not new or novel. Complaining that not all entities have the same powers isn't going to get very far.
[1] Ligier's light when he turns his scornful gaze on Malfeas to purge an affront from the world... is environmental damage and thus no-sold by a bunch of Exalted defences. And that means that if you survive that, he then sends the Sword of the Yozis down to fight you in the middle of a firestorm, on a place where the metal buildings are melting and the entire area is irradiated by Green Sun Wasting. And then if you beat the Sword of the Yozis, he descends to fight you in person to have a kung fu fist fight.
[2] Or, you know, they can get into a similar ballpark with the max level Shintai, like the Greater Shintai of the Endless Desert which can destroy cities by making you into IMOTEHP SANDSTORM... and which is also similarly bad at fighting Exalts.