In my opinion, and it's only an opinion based on my own results and experience, placing new content on secondary pages is perfectly fine provided that there is a clear navigation route from your home page to the new page(s) you post.
Think about it, before blogs became the "in thing", the vast majority of sites grew in exactly this manner. When there was new content to publish, the site owner created a new page for it, and as long as there's a simple navigation system in place that keeps the new page(s) within a couple of clicks from the home page, the search engines would find it and index it just fine. It was also a good idea to have a sitemap in place too, but not absolutely necessary if your navigation system is clean and simple.
That still holds true, it's just that people have become so used to blog-based site architectures now that they almost expect fresh content to appear on the home page frequently.
That isn't what fresh content means. Fresh content means you add new, and hopefully meaningful and valuable content to the site on a regular basis, not necessarily the home page or any other page, but to the site as a whole.
Search engines just want to see evidence that the site is actively maintained and when they do they will hit it more often with their bots and show it a bit of love in the index. You can achieve this with either pages that frequently are updated (like editing a home page often or using a blog CMS), or by adding new pages to the site on a regular basis.
HTH