The only downside I can think of are firstly that the water pressure for an attachment one can be painful if you turn it up to fast at first if you haven't gotten used to the knob. I did buy a cheap one without hot water at first but ended up buying another one with hot water as well. I'd be fine with the only cold water one, it's still 1000x better than toilet paper, but the hot water is nice in the winter. It's also annoying to clean around somewhat.
I guess I don't really fit the description in your title though, those are the downsides I can think of with mine though, also mine were the bidet attachments, not a full bidet.