No. The Russians simply were severely outnumbered by Ukrainian forces in the Kharkiv region. Different circumstances there.
Why is it that it's the Russians who find themselves severely outnumbered. Or more accurately, the number of Russians willing to fight were severely outnumbered by the number of Ukrainians willing to fight. Why is it that since mid-summer 2022, it's the Ukrainians who make the big gains, capturing hundreds of square miles at a time, with minimal artillery support, with minimal casualties, while the Russians can only gain a few yards a day, and need massive artillery to do that, while taking heavy casualties.
Where is the equivalent Russian victories in the last six months comparable to the Ukrainian victories to the east of Kharkiv and at Kherson? Answer, there are none. Why? Because Russia is losing the war.
What is the glue that holds the Russian army together? It's not the Wagner group. It's the mud. And the mud is not going to last forever. In 2023, we will see the sort of advances from Ukraine that they had in September, when there was no mud to bog down the Ukrainians.
Why can Ukrainians hold on the the far side of a river, like at Bakhmut, but Russians can't, like at Kherson?
Crimea is a peninsula with a large naval base, air bases, anti-aircraft defenses, etc. And most Russians have long viewed Crimea as part of Russia. Meaning, it's a non-starter for Putin to give up Crimea they way he gave up Kharkiv and Kherson City.
Most Russians support peace talks but reject return of Crimea, poll finds
https://www.washingtonpost.com/world/2022/12/13/russian-poll-peace-crimea/
"Seventy-eight percent of Russians said it would be unacceptable to return Crimea to Ukraine, while 66 percent said the same of the eastern Donbas region, which remains occupied by Russian forces and their Ukrainian allies."
Doesn't matter. Holding the far bank of a river at Kherson is child's play compared to holding Crimea. You have to have a way to get supplies into an area to hold it. You have to, or it cannot be held.
How can Russia possible get supplies into Crimea? Only one of two ways:
1. The narrow corridor, called the "Land Bridge" that is just to the north of the Sea of Azov. The Ukrainians should be able to cut that off, possibly capturing a good hunk of the Russian army with it's back to the very shallow Sea of Azov.
2. Across a wide strait to the east, with only one bridge across it, and that bridge is not like the multiple bridges of Kherson, just a few hundred yards long, but many miles long.
If they can't supply an army on the far side of a relatively narrow river, with many crossing points, how are they going to do so across this wide strait?
It's not going to matter if Putin and the Russian people feel they must hold Crimea. If they can't hold it that can't hold it. The Russians will have a far easier time holding the Ukrainian stripe of territory along the Russian border in the Donbas region. That is much easier to supply. Crimea is not going to be so easy.
Soledar and Bakhmut are important logistics hubs for Ukrainian military in eastern Ukraine. Losing those towns/cities makes it more difficult for Ukraine to launch a new offensive in the East. It puts them on the Defensive.
I don't buy the notion that suddenly seizing a thousand square miles of territory in a few days, with few casualties, is of little military import. While seizing, what, five or ten square miles of territory, over a period of weeks, while losing far more casualties, is somehow of much greater import? Nope, I don't buy it.
Of course, I could be wrong but if those cities are so unimportant, why has Ukraine sacrificed thousands of troops to hold them? It makes more sense to withdraw from areas that aren't worth defending and can easily be taken back later. But instead, we've watched Ukrainian forces suffer massive casualties defending the Bakhmut-Soledar region over the last few months. Seems like it's more important to Ukraine than you think.
Why?
1. Because the Russians, making World War I like infantry frontal assaults on trenches, are suffering a lot more casualties than the Ukrainians.
This is not the way to win this war. The way to win the war is to make a sudden decisive breakthrough, that allows your forces to advance many miles in a day, with far fewer casualties, like the Ukrainian September offensive east of Kharkiv. That's the formula that the Russians have not been able to follow since last spring.
2. Because the Russians are hoping for some sort of victory, that can fool the Russians into thinking that they might be able to win the win. Which might inspire hundreds of thousands of Russians to start volunteering for duty at the front. As hundreds of thousands of Ukrainians volunteered last February. This is a fools' hope. But, why give the Russians any air?