You are right that PHP can do the feed checking part but I wanted to use something with easy async/concurrency out of the box (and wanted to learn Elixir instead of using Node.)
One hard tech limit is that with 50k podcasts, 4million+ episodes, search definitely doesn't work well. Not just WP, but SQL itself. Hence Elasticsearch. I also plan to work on recommendations, etc. so will need probably to be exporting SQL data into other systems anyway for making the "people who liked this also liked this" kinda things.
Also I kinda lied about using the WP API--that's how I built the system initially (and will switch to it moving forward), but to import the first few million posts from the content of the feeds, I just used wp_insert_post against the DB of new entries that Elixir fetched (I posted the code I used here: http://wordpress.stackexchange.com/a/233786/30906).
I also plan to write the whole front-end in React (including server side rendering) so will have to figure out how to get that done. Would probably use the WP-API with a Node.js app in front of it, will look into hypernova from AirBNB. So probably more usage of WP API accessed by another service...