During 1941 the Red Army was pretty much collapsing. The only reason the Soviet Union stayed in the war was because it was that big and the forces could lose land without fatal consequences for the war. An advantage which Poland, France and Greece did not have. The Wehrmacht for instance had also skyrocketing KIA and MIA in the last months of the war. If an army loses the order and gets overrun the casualties get disproportional. People without proper training get rushed into service. Supply chains don't work, communication gets cut, commanding officers get killed. Chaos.
In 1941 the Wehrmacht had operational and tactical superiorty over the Red Army. This means despite the overall strategy of Germany not working the major operations were mostly successful until Taifun. This resulted in massiv Soviet casualties by collapsing Armies in pockets and armies which lost cohesion while retreating without order. From 1942 till the end of 1944 the Wehrmacht was only able to keep its superiorty on the tactical level. This means smaller units would outfight their opponents and inflict heavier damage, this is true for all branches Infantry, Armored units, Luftwaffe et cetera. This would lead to heavier casualties but favorable results on the strategical scale for the Red Army.
The reason for this are diverse but one of the biggest factors is the average officer. The German officer was very good trained and the methods of the Wehrmacht were state of the art. Many officers of the Wehrmacht were long members of the Wehrmacht and before that the Reichswehr. The German soldier was proud of its job and the strong focused propaganda from 1933 on created very motivated soldiers. On top of that the Red Army purges increased this disparity leaving their forces with weaker officers. When Barbarrossa hit the Red Army a big chunk of the Soviet forces got destroyed including many experienced officers. The armies which now got raised in Russia were at a serious disadvantage in terms of experience. If you think about the average Soviet officer. He got maybe already killed during the purges if not he was maybe a yay sayer who didn't want to become a victim of the purges. Obviously there were capable Soviet officers but there is a good chance these soldiers were sitting in briansk or kiev when the Wehrmacht overrun the Red Army in 1941. At this point many good experienced soldiers were gone. Now in 1942 how is the situation on the front? You have newly raised armies with green officers who have to fear for their life if they make mistakes. Who are these armies fighting? The Wehrmacht soldiers/offficers who already fought in Poland, Norway, Low countries, Greece, Yugoslavia, Belarus, Yugoslavia et cetera. Always victorius, bonded together and highly motivated. The Wehrmacht in 1942 was the most experienced army on the planted without a close second. They had the most experienced soldiers/officers which were trained with best available methods and were supplied with mostly superb equipment. Its impossible for the Red Army to challenge this superiority on level of small units. The Red Army can't overcome this quality disparity. The only option is overwhelm the enemy by attrition. The Soviet Union understood this very well. During 1942 the mobilization effort was unprecedented. During the war about 60% of the entire population was either marching in the Army or working directly for the war effort. No other country came close to that during the war.
Furthermore the Soviet Union and their leaders had a different approach to fighting the war than the USA or the United Kingdom. Advancing fast was preffered to advancing safe. The Western Allies would rarely "force" breakthroughs with casualties. This led to slower advances but moderate casualties. Take Normandy for example. Despite considerable force ratios the 21st Army Group advanced slowly. Support of Artillery and heavy bombers was used very often for rather short land grabs. A good example for this Goodwood.
About 7000 tons of bombs were dropped on mainly two divisions. The amount of bombs and artillery dropped on the German front lines is mind boggling. Than the forces would advance round up the demolished 16th Luftfeld and start hitting resitance from German reserves. At this point the casualties start rising because the German ground forces get their order back and the organized resistance increases. After just 2 days the operation gets stoped. The damage dealt to the Germans was considerable a big chunk of that due to the bombardments. The 16th Luftfeld was obliterated during the bombings and shelling. The British forces advanced about 10 Km. Thats not alot for major offensive with such ressources. The amount of ressources used is of the same magnitude of the German attack during the Battle of the Bulge. Why is that? By doing this the casualties for the British forces are lower than they would be if they force a breakthrough. The use of artillery and bombers inflicts serious damage to the German forces and the first attacks of ground forces multiplies the effect of the bombing when it hits the units which lost order during the bombing. When resistance increased the operation ends. Repeat.
Thats not how the Red Army handled offensive. The Red Army would press advantages and try to collapse the German front because the Soviet leaders knew they could defeat the Wehrmacht this way. The Wehrmacht would use it reserves to counter attack if this is not enough they have to retreat. If it goes real bad they have to retreat with out order and parts of the front collapse. Happened during Bagration. The Red Army casualties are in line with Soviet expectations and the overall strategy. German Armies can't sustain these casualties and lose. How long would the Red Army attack? Either until a objective was achieved, the supply chains were stretched, the Germans would launch "successful" counter attacks or the percieved threat of over comminting was to high. They improved this over the war if you take the southern wing of Kursk for example the massiv Soviet offensive would first stop when heavy German counterattacks hit the soviet Spearheads and wrecked havoc. Over streched supply chains, exhausted troops now momentum left underestimated counter potential. Later in the war this happened less and less and the perfect timing for consolidation the gains was often found and a new offensive was planned. Attack preferable the entire front with one focused sector to avoid shuffling of Wehrmacht troops. Force breakthroughs, accept casualties and exploit the situation until the momentum is gone.
Why would the Red Army not advance slower? First of all its questionable if the Red Army has the same amount of ressources of bombs and artillery to achieve the same effect like the western allies. Keep in mind, slow advances wouldn't bring the Wehrmacht in the same trouble because Soviets number advantage wouldn't get the same impact, thats why you see full front attacks during 43/44. If you advance slowly one operation at a time, the Wehrmacht shuffles its forces. Furthermore the Red Army had more to gain by advancing than US/UK. New soldiers for their armies drafted from liberated areas and new ressources. More post war impact in eastern and middle Europe was also important.
Back to Normandy. Could the British force breakthroughs? Yes they had so much ressources at hand but the time right before the final breakthrough is when the casualties are the heaviest. The defense is organized, well conciled and knows quite well what opponents wants to achieve. On top of that a "breakthrough" opens your units up for counterattacks into the flanks and rears which might result in a pocket which is pretty much worse case szenario the nightmare of every commander.
It should be noted that the Red Army is underestimated by many amateur historians. The Red Army faced the most efficient army and had to start from scratch when their western armies got overrun in 1941. When the Red Army attacked other axis members it often had no problems at all. When Uranus opened the Romanian and Italian armies were swept aside within the first days. During Winterstorm the German reliefe attempt was ended by again collapsing Italian forces which were the flank protection of the offensive. The Red Army repeatedly overran Axis members. Finnland aside. When dealing with German armies the difference on small unit level was just too big to catch up. The Wehrmacht advanced their methods and technology so the Red Army despite considerable improvements was not able to catch up partly explaining the higher casualties. This sounds cruel but it should be understood that the casualties were calculated and tolerated for the overall strategy which resulted in victory for the Red Army.