I really, really wanted to intern in the House or Senate while in college but it was completely unfeasible due to not only the costs incurred while living in DC, but also the lost opportunity to make money that would pay for expenses during the following school year, such as books, transportation, and discretionary spending. I consider myself incredibly lucky that instead I found different internships two years in a row in DC that provided housing and an actual salary. Unsurprisingly, I ended up in a career much more similar to my internships related to data science & statistics instead of politics. Looking back, I consider that a giant bullet dodged. Whew.
I should also add that the exclusionary nature continues beyond internships, as paid staff positions in Congress have super low salaries — something along the lines of $30K. That pays rent in a crappy shared group house with very little left over…. most people I know that ended up working there right after college were being subsidized by their parents.