Those trunks don't look like they belong to birch, FWIW. They are very beautiful. I love great vertical features like that; what a statement!

I am a firm believer that empty space is a very important design element in landscaping. Rather than being "dead", voids have the role of accenting the existing plants, emphasizing their importance and, in your example, beauty.

As a professional designer, I always included mulched voids to emphasize important elements. It's especially effective in small areas such as yours. Adding plants just for the sake of filling in the space is likely to result in a messy, and distracting appearance. Visual clutter.

Why add something to that location that will require maintenance, water, hand weeding, etc?

Just my measly opinion, but do think about it.