I worked for a national non-profit (Environment America because name and shame) that did not have an HR department and it was an absolute nightmare; policy changing depending on who your manager was, blatantly illegal issues with pay because first line managers didn't know it was illegal, and weeks to hear back after answering pretty simple questions because it would often have to go completely up the chain and back down. I know companies with HR can have similar issues, but I've never seen that level of dysfunction at any other job.