Seminoles do have contra rotation props (an O-360 and an LO-360).
A big reason you lose so much performance is you have to add a lot of drag to counteract the torque from a single engine beside you. You get added lift from the prop wash (accelerated air over the wing from that engine), which you have to counteract on the other wing (more drag!) and then you have to add a bunch of rudder (which is a BUNCH of drag!).
Larger aircraft (such as a baron and up) tend to have larger engines that can take it. A seminole will climb empty, but isn't all that great... and the problem isn't just its performance, the performance isn't what gets you, it's that if you try to get more than it's capable of it can kill you... you get behind the power curve, and then performance decreases when you increase pitch, you keep pitching back to get more performance and it gets worse until eventually you stall... not good at all when you have full rudder one way with full power on the live engine...
The biggest thing you have to train for is the idea that even at full power, "blue line" (VYse, which is described on the airspeed indicator with a blue line and is the best climb rate you can get single engine) might not even let you maintain altitude. It's the training to let the aircraft descend if it wants to (even if it means setting down off airport). What gets people is the thought that they have to make an airport because they have a running engine. Sometimes you just have to swallow your pride (and there are many such situations in aviation).