The maps do not really put things in perspective.
There is a massive difference between the areas in the North previously occupied by the Russians and the areas in the South, in particular the Donbas, Kherson and Zaporizhzhia (which Kharkiv is not a part of).
The Southern Donbas to Kherson band is of obviously political and strategic importance: Donbas being the pro-Russian separatist region supported by Russia (and at least nominal cause of the whole war), Kherson controlling the canal that supplies water to Crimea and Zaporizhzhia is the region directly in front of Crimea (additional protection and connects to the other regions for supplies).
Russia conquers nearly all this additional territory in the South in about 3 days and then there is prolonged siege of the Azov battalion and other forces in Mariupol.
There is obvious political and strategic value of these regions, Russians conquer nearly all of what they currently have in a matter days, and still hold it and clearly are willing to defend it as we see in Kherson over last few days.
The Northern operation was very different. Russians simply went around towns and tried to surround Kiev.
Analysts kept on telling us it would take at least a million soldier army to occupy all of Ukraine, which the Russians didn't invade with ... well, they invaded with 200 000 soldiers and are now occupying 20% of Ukraine, so maybe the math checks out.
The operation in the North was quite obviously to achieve 3 things:
1. Ideally the capitulation of the Ukrainian regime (accepting the offered peace terms) with the pressure on the capital]\.
2. Failing that, fixing Ukrainian forces in the North to be unable to defend and/or launch counter-offensive in the South (before new fortifications, supply lines setup and towns passified, there is vulnerability to counter-attack).
3. Destroy industrial capacity and various targets around Kiev, which apparently is achieved.
Now, whether doing the above was a good strategy or not is one question, but there was obviously never any even remote attempt to storm Kiev or occupy all the Norther regions the Russians pass through.
How likely the Kremlin believed in Ukrainian capitulation I don't know, but obviously there was plan B which was take in the South the desired lands and strategic locations and destroy Azov Batallion (whether the Kremlin genuinely fears/ despises these neo-Nazi's is one question, but either way it is critical for the home audience to defeat Azov Batallion in particular).
In particular, now that all pro-Ukrainian propaganda is instantly declaring the Kherson operation a fixing attack ... it's just dumb to dismiss off-hand the Kiev offensive as not possibly a fixing attack but failed occupation of the North and storming of Kiev.
As for whether it was a good idea or not, Russian generals have several nightmare scenarios at the start of the war:
A. Being stopped coming out of Crimea and the entire Southern operation falling flat.
B. Even after the South operation succeeds, successful counter attack that (for example) creates a salient to Mariupol and breaks the siege (as well as just counter offensives generally speaking).
Had A or B occurred it would have been a massive embarrassment to the Russians.
Certainly some things have gone well and other things less well for the Russians, but they have not experienced anything like an actual military debacle. Propaganda needs to spin full tilt just to present Ukraine as "in the fight", so imagine if they had just shelled to rubble the bridges out of Crimea and the Russians never got out of there, or valiantly penetrated Russian lines and fought all the way to breaking the Siege of Mariupol.
Keep also in mind, that there is not only these purely strategic elements in the South described above, but that's where Azov battalion, of which defeating is absolutely essential to the entire de-Nazification enterprise. So, failure to take this region would have been completely disastrous in terms of international and domestic image (support for the war etc.).
So, considering the stakes in the South, it is entirely logical to commit forces to threaten the capital which then must be defended at all costs (liquidating Azov battalion maybe a priority for Russia, but keeping Kiev would be the priority for Kiev; so one priority for the other).
Of course, would have been even better for the Russians if Ukraine simply collapsed, accepted peace terms etc. but a military strategy does not take into account political resolution; that for politicians to do or not, military planners will assume there is no political resolution to the conflict in elaborating their plan -- if they are told not to try to take all of Ukraine, they will then simply plan for an eventual frozen never ending conflict a la North-South Korea.
Point is, whether the plan was the best, could have been better, should not have been launched in the first place etc. are all valid criticisms, but the criticism that the plan does not make sense or has already failed is simply not supportable.
Additionally, even for the Russians to withdraw at this time, it would still be less embarrassing than being stuck in Crimea or Azov Battalion being rescued.
Russians have (even if they withdraw now) demonstrated the massive amounts of man power, equipment and money required to deal with (200 000 of) them. From purely international relations perspective its not "so bad" if Ukraine has clearly paid a heavy price for the withdrawal (that no other rational party would want to pay). One cannot draw the conclusion that the Russians are push-overs, certainly neither the Ukrainians, but this doesn't necessarily encourage anyone to seek conflict with Russia anytime soon.
However, I very much doubt the Russians will withdraw and until Kherson West of the Dnieper is reconquered by Ukraine I have a hard time believing they have the offensive capabilities to seriously threaten Russian presence East of the Dnieper.
The regions the Russians are committed to holding have now dense and integrated fortifications, concrete shelters for tanks, bunker networks etc. electronic warfare setup, and is extremely hard to assault, as the recent offensive in Kherson demonstrate.
Russian tanks emerged from newly built cement fortifications to blast infantry with large-caliber artillery, the wounded Ukrainian soldiers said. The vehicles would then shrink back beneath the concrete shelters, shielded from mortar and rocket fire.
Counter-battery radar systems automatically detected and located Ukrainians who were targeting the Russians with projectiles, unleashing a barrage of artillery fire in response.
Russian hacking tools hijacked the drones of Ukrainian operators, who saw their aircraft drift away helplessly behind enemy lines. — Wounded Ukrainian soldiers reveal steep toll of Kherson offensive
Yes, offensive in Kharkiv (not part of Donbas ... no strategic importance to Crimea) did succeed, but none of the above was put in place.
The reason to tactically retreat from a region you are not intent of occupying long term (whatever the reason: political, terrain and/or man-power) is to save as many of your own troops as possible while inflicting significant casualties on the advancing army: artillery, mines, gunships, missiles and bombs in predetermined kill-zones.