Your question is framed as if any model of glaciation were only allowed to consider one of those influences. I think practically any palaeoclimatologist would accept that astronomical forcing, solar output, and volcanic eruptions all have effects on glaciation. It's true, however, that on long timescales (tens of kiloyears and up), Milankovitch forcing generally gets more attention than the other two you mention. There are further important drivers of glaciation which you don't mention. Perhaps the most obvious is greenhouse gas concentration: if atmospheric levels of CO2, methane, and other greenhouse gases drop, the Earth cools and glaciation becomes more likely (see e.g. DeConto and Pollard, 2003). Another influence is tectonics and geography, the best-known example perhaps being the theory that Antarctic glaciation was caused by the break-up of Gondwana, which left Antarctica thermally isolated (Kennett, 1977).
To return to your main question, there's a good reason to consider Milankovitch forcing as a (or the) dominant driver of glaciation on longer timescales: it's simply that glaciation (as deduced from δ18O records) varies in time with the astronomical cycles. Hays et al. (1976) is one of the classic papers on this, and they sum the situation up neatly:
Over the frequency range 10−4 to
10−5 cycle per year, climatic variance of
these records is concentrated in three discrete
spectral peaks at periods of 23,000,
42,000, and approximately 100,000
years. These peaks correspond to the
dominant periods of the earth's solar orbit,
and contain respectively about 10,
25, and 50 percent of the climatic variance.
To put it another way: if you want to discount astronomical forcing and attribute those variations to (say) volcanic aerosols, you need to explain why you have volcanoes going off at precise 42,000-year intervals. This isn't to say that we fully understand how these drivers interact with the climate system yet (the 100,000-year problem is perhaps the best-known "wrinkle" in the theory), but the fact remains that if your glaciations are dancing to 23, 42, and 100-kiloyear beats, and your solar system happens to be providing beats at precisely those frequencies, there's probably a pretty strong connection there.
- DeConto, R. M., & Pollard, D. (2003). Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric CO2. Nature, 421(6920), 245-249.
- Hays, J. D., Imbrie, J., & Shackleton, N. J. (1976). Variations in the Earth's orbit: Pacemaker of the ice ages (PostScript). Science, 192(4270), 1121-1132.
- Kennett, J. P. (1977). Cenozoic evolution of Antarctic glaciation, the circum‐Antarctic Ocean, and their impact on global paleoceanography. Journal of Geophysical Research, 82(27), 3843-3860.