There are no major models that come to the conclusion that idiosyncratic risk can drive positive returns. The reason is that idiosyncratic risk is diversifiable. The models, however, do in fact consider idiosyncractic risk. The theories don't forget or ignore them. It just turns out that this risk doesn't matter.
In this sense, CAPM actually does consider idiosyncratic risk. In this model, if you are perfectly rational, you will diversify your portfolio to minimize risk. This leads you to hold the whole market portfolio, in which case idiosyncratic risks are diversified away in your portfolio and therefore no longer matter. In simple terms, market risk then is not diversifiable, because once you hold the market portfolio, there's no way to diversify further. What drives returns are risk, but rational investors can remove the idiosyncratic risk through diversification. Hence, what matters for returns in the CAPM therefore is just the market risk (which you refered to as systemic risk, but that term actually means something else). That's why under CAPM, the returns are driven by the asset correlation with the market.
The CAPM model does not put any explicit assumptions on the number of assets available, hence the model does not require an infinite number of assets. However, the derivation is based on the decision to add an asset to an already well-diversified portfolio, i.e. adding an asset to the market portfolio.
Nevertheless, if only a handful of assets exist, then it might not be possible to diversify away all idiosyncratic risk. In that case, the CAPM does not work, because it implicity assumes enough assets exist, since it assumes a well-diversified portfolio exists to which you can add an asset. In such a case idiosyncratic risk may become relevant.
Such considerations are unlikely to be relevant in practice though. It is difficult to put a number on how many assets are necessary for idiosyncratic risk to be diversified away completely. Often, a number that is mentioned is 30-40 assets. The number required in practice is usually very realistic and far below infinity. The number of assets required for idiosyncratic risk to be completely diversified away becomes larger if assets are more correlated with each other or very volatile.
Lastly, an asset with such high idiosyncratic risk that no investor would want to add it to their portfolio cannot exist in equilibrium, because supply of the asset could never equal demand.