No matter how you build them, nuclear Radioisotope Thermal Generators are heavy.

That's totally inaccurate. I went into details about this a couple days ago when Philae was discussed here. In that case someone said that because it took 10 years to arrive at the comet, an RTG couldn't have been used. I'll just copy/paste my other post since it already covers your statement.

The lander only uses 32 watts of power. The MMRTG used in Curiosity provides 125 watts of power initially, and 100 watts after 14 years. The mass of that specific RTG (the MMRTG, 45kg) would be too great for use in Philae, but then it also produces 3 times more energy than needed (even after 14 years). RTGs have been made in many sizes for many different applications, so it would simply have been a matter of designing an RTG that produces 40-45 watts of power after 10 years.

However, one of the main uses of the 32 watts of power required by Philae is just to keep the batteries warm so they don't fail. RTGs produce more "waste" heat than they do electricity. For example, the MMRTG used in the Curiosity rover produces 2 kW of heat, of which 125 W is converted to electricity. The extra heat is used to keep the various temperature-sensitive parts of the rover nice and warm so they don't fail. With Philae, a good portion of the 32 watts of the solar power it requires is just to keep the battery warm. So if an RTG were used, it wouldn't even need to produce 32 watts of electricity since it can keep the lander warm directly.

Looking at the mass and wattage produced, the RTGs ("SNAP-19") in the Pioneer probes would have been just about perfect for Philae. They produce 40 watts of power and weigh 13.6 kg. Philae's current electrical system weighs 12.2 kg, so that's at least in the ballpark. The RTGs on the surface of the moon, as manually placed by Apollo astronauts's would have been a bit heavy at 20 kg. One of those RTGs was still producing 90% of its power after 10 years.

The SNAP-9A used in the Transit 5B-2 navigation satellite launched in 1963 weighed 12.3 kg and produced 25 watts of power. That looks about like a perfect fit for Philae, and I'm sure more efficient thermocouplers are available today that could further reduce the weight.