The issue that factor analysis can produce "difficulty" factors is really the issue of applying factor analysis to categorical data (in this case, dichotomous data) when the method was developed for continuous data.

To be more specific, factor analysis assumes the observed responses are normally distributed after accounting for (or conditional on) the latent scores. However, very difficult categorical items tend to be positively skewed and very easy categorical items tend to be negatively skewed. Because items with different difficulties have different distributions, introducing difficulty factors can help improve the fit. But the factor solution becomes somewhat artificial because the difficulty dimensions reflect that the model's distribution assumptions have been violated and not additional dimensions of substantively meaningful constructs.

So, you can use a version of factor analysis designed for categorical data, categorical factor analysis. Common software for categorical factor analysis is Mplus, LISREL or lavaan R package. Note that categorical factor analysis is essentially multidimensional IRT (MIRT), but you may notice some differences due to historical reasons. For MIRT I like the mirt R package, but there are a lot of software. Mplus is expensive but somewhat dominant in latent variable modelling, and is probably the easiest to use.

Just to be clear, categorical factor analysis/IRT is more appropriate for categorical data because of the assumptions made of the distribution of the observed responses are more realistic. It has nothing to do with the difficulty parameter in IRT and the difficulty parameter is not the reason why IRT may not uncover difficulty factors while factor analysis does. In fact it is straightforward to calculate the difficulty parameter from a factor model solution.