As others have remarked, it's not that they didn't want to, as the existence of strategic bombers proves. In fact, I think the first attack on Berlin was shortly after the opening of Barbarossa, and the Rumanian oil fields were targeted too early on. But one problem is that the worthwhile strategic targets quickly came to be very far from the front lines indeed, and bombers suited to the task thus had become fewer. And when you are fighting for survival, and have a long front line, investing a lot in a strategic air arm dosn't make a lot of sense. That's one thing to explain the symmetry in Germany and Soviet focus on the areas near the front line.
I think I've said it before somewhere, but strategic bombing dosn't refer to four engined bombers, or even neccessarily to a specialized bomber, it depends on the kind of target you are hittiing. Some strategic bombing may be possible with medium bombers if you have enough close enough. But of course there are bombers better suited to the task than other, and usually these are worse suited to tactical bombing.
Time to stop repeating myself (provided saying it, in the first place, isn't one of my fake memories), I have som remarks on advantages to tactical bombing, or strike, that are so iconoclast that I'm sure I haven't dared to air them before.
It sets off from the admittedly simplistic notion that strategic bombing often aim at bottlenecks however those are percieved to be, ball bearings, fuel production or public morale, to name a few. Ideally you want to throttle your enemy as quickly and cheaply as possible, but rightly identifying the targets and assessing the damage needed and done are complicated. It can be argued that the allies could have conquered Germany from the air only, had they proceeded with this or that plan. It may be true, but the point seem to be that even with overwhelming force and the ability to read much of the enemys communications and photograph the targets after the raids, they didn't quite succeed.
When you start out hitting bottlenecks, hitting the neck can be difficult. Lets say the enemy produce 100% of what is needed to build and operate of wheels, armour plate, ball bearings, radios, fuel, cannons, mashine guns, ammunition and crew 100 tanks.
Now you hit the ball bearing production for 50% of its capasity, well and good, the enemy fields 50 tanks. Then, to keep targets varied and because of whether and contingencies and the rest of the ball bearing factories are more difficult targets, you hit the fuel production for 40%. Ouch, but the nemy still fields 50 tanks. Hit it for 50 fuel, the same goes. Hit all of the parameters for 50 simultaneously, it is still 50 tanks. And bear in mind that bottlenecks pop up independent of bombing, maybe lost territory redused one or the other, or bad planning. You simply cannot predict your target with 100% chance of success.
Then take a tankbuster, even though I agree with those who suggest they were not that effective. Anyway, if they kill a tank, they take out a whole package. One tank entirely lost is sure to hit whatever of the parameters is the bottleneck. And the effect is immediate. Kill another kind of system, and you are sure to hit the bottleneck in that one.
A war time economy is complex, and ball bearings aren't only used for tanks. Hit the capacity 100% percent, and all kinds of stuff stops moving. Once the stocks are used up, that is. Did you assess those correctly? But factories hit does hurt, also future planning, though it is difficult to attain maximum efficiensy. So hitting stuff while it is on the battlefield, also because it mattters whether a battle is lost or won, can be very useful indeed.
But if one looks at it in a cynical way, one reason that Germany and the Soviet union focussed so much on the front lines is that it suited, to some extent, the weapons they had at hand. Normal medium bombers aren't really ideal for battlefield support, and note that I entirely left out interdiction, an important category as well. But boy did they had a lot of common front line.
Churchill, on the other hand, found that he (or Britain) had committed to an stupendous program of making heavy bombers, and so chose a strategy that fitted the weapons at hand. As also the lack of an endless front line suggested he should do. And if you can't hit ball bearing factories with kirurgical presission at night, you convince yourself there is another bottleneck. it has nothing to do with a wish to win the war in a nice or a nasty way, but simply what you can do with what you have now. Pre war choices influenced the strategy chosen, but geopolitical realities also, to some extent, dictated these pre war choices. some of them undoubtedly were questionable, but we're all human.
On the global basis I think one factor behind the allied success was that they had the resources, and the theaters, to make use of all kinds of bombing, and between them the capacity to design and build all categories of bombers, from Il-2's to B-29's. The axis were simply too spread thin to match or counter that. add to that the need to mass produce fighters that are good at sea level, excels at ten kilometers and beats everybody else at medium attitude, fly to New york and back and have a useful second role as ground attack and recconaisance and night fighters, spew a lot of light bullets for dogfights and heavy cannon shells for downing bombers. I think any of the 3 great, had they had to go it alone, would have faced the same kind of problem. Instead of speculating what kind of bombing could have won the war by itself had 'we' built more divebombers in 39, or more 4 engined bombers in 42, is futile. It's rather how the different categories complimented each other, and stretched the enemy, that was significant. Stalin could afford not to lay the German cities to waste, somebody else was already doing that.