All Segments

How many segments are you wanting to report on?  How many metrics would you include?

My initial thought would be to build out a workspace project and schedule it.  This is just a quick wireframe based on sandbox data.  But I'd start by trying something like this.  I removed totals, grand totals, percents, and sparklines to clean things up a bit.  Since this is demo data, some doesn't make sense, but this approach seems easiest to me.

Report builder and Workspace are the most efficient ways of exporting metrics for all segments with your daily data.

Create your report as per the requirement and schedule it on daily basis.

You can add multiple segments in the dimension and add your metrics and schedule your report accordingly.

I'm with @josh__stephens on this one... depending on how many segments and metrics you are talking about, and how often you need to roll in new segments, a scheduled workspace might be the easiest to manage.

With Report Builder, there's the complications of constantly having to build new requests and getting them formatted, then having to cancel the old schedule and create a new one.... (since re-saving a Report Builder doesn't update the copy on the server and send the new data).

With APIs, you have to know all the Segment IDs and build the jobs and a place to store the info.... 

But again, there will always be caveats to the options, and reasons why a solution may be easier for you.