Couldn’t agree more. We have lived with the birch for the last 7 years we’ve been in the house and it is messy. Leaves a nice rust colour stain on the coping and deck and springtime is a PITA with the pool getting filled with Crud. So out it goes! (The landscaping company is taking it out).Looks like a nice plan. Unless there is a really good reason to keep the existing birch on the right side (say for privacy from a two story home behind you) I'd remove it. Birches have shallow root systems and you are asking for trouble with your deck in that area. Not to mention it's pretty close for debris. Birches aren't the cleanest of trees. You don't notice it much when there is grass below them.