A radio was "standard equipment" in the T-34. Some tanks were produced and deployed without their radios due to shortages, but it's not because they weren't designed that way. More importantly, problems with the radios and lack of spare parts rendered the vast majority of them inoperative in short order, so the bulk of the tanks in the field were left with no functional radios, and had to maneuver based on signal flags or simplistic "follow the leader" tactics. Internal communications systems were no more reliable (or inaudible over the normal engine noises, in the rare event that they actually worked), so the tank commander usually had to deliver directions to the driver by means of foot taps on the shoulders. Take those crippling internal and external communications problems and add limited visibility and situational awareness to an already stressed and poorly trained tank commander's multiple roles when the shooting starts, and it's a recipe for disaster. In essence, the whole armored formation was often fighting all-but blind.
The T-34 was a radical tradeoff of strengths and weaknesses, with a few excellent features that made up for some of its serious flaws (big gun for its intro date, wide tracks, and sloped armor, versus cramped interior, 2-man turret, poor visibility, poor communications, unreliability). The combination proved effective enough for the Soviets' situation when deployed "en masse", at least after the catastrophic leadership and training issues were addressed, but I would not have wanted to be in one of those tanks in a combat situation. If that's a "great tank", I'll gladly take an average one instead.
Germany faced daunting materials shortages, so any military equipment designs had to account for the fact that certain materials would be in short supply. The Germans could NOT have built their own T-34s in any significant quantity, because the materials were simply unavailable. They could also not build anywhere near the sheer quantities that the Allies could crank out the door. The Panther was a compromise design based on what materials the Germans thought they would have available, and the design reduced the amount of rarer materials needed at the expense of adding more sheer mass of weaker metals, and more complexity. They were overly optimistic on availability, so additional corners had to be cut for later production. The result was an overweight and unreliable tank, because that was about the best that they could do under the dire circumstances. The Panther's own crew visibility was decent in comparison to that of the T-34, but no longer sufficient compared to developments on the Western Front. In hindsight, even more reliance on turretless designs (StuGs, PanzerJaegers, JagdPanzers, etc.) might have been better, which both Germany and the Soviets were utilizing in growing numbers, but that may not have been fully apparent or appreciated (especially by what's-his-face at the top) at the time. Sticking with the Panzer Kampfwagen IV design, which had already reached its limits for suspension loading and engine size, might have been semi-viable for another year or so, but like the T-34 after the first couple of years, it had already become "average at best" on the battlefield, and Germany couldn't afford to trade "even up" in casualties. Germany needed a "superweapon" to avoid or postpone inevitable defeat, and the Panther was the closest they could come to one, but it fell well short of the mark for a long list of reasons.
The Soviets could have, and eventually DID come up with a better design than the T-34, which was only considered an "interim" design in the first place. I don't think that Germany could have come up with a "great" tank in their situation, but the Panther could have been pretty close if the materials had been available to correct (or avoid in the first place) several of the most serious weaknesses (some of which had already been identified and addressed, but were never "fixed" because it was not feasible under the circumstances). The M4 Sherman is an example of what you can do with virtually unlimited resources, sufficient production capacity, and all of the engineering expertise that you care to throw at it, and it's still not a "great" tank, but a very good one with almost no specific weaknesses after the initial "trial and error" introductory phases. As pointed out, the value of a design depends heavily on the situation of the country that's using it, and what works for one may be poorly suited for another.