This obviously works, you can even use iTunes as the source of the RSS feeds, there's not really anything proprietary to how Apple did podcasts, its just a database of the RSS feeds - just right click the podcast search result in iTunes and click "Copy Podcast URL".
However, copying RSS feed links is a pretty terrible way to discover content. Most normal people want a search or recommendation engine of some kind (you liked x, you will probably love y), which is why virtually every podcast app offers access to searching some kind of RSS feed database of podcasts within the app.
If you were to go with your approach, I'd personally still consider using iTunes as the search engine for the RSS urls, most podcast app makers seem to agree Apple's database is pretty much the most complete out there, probably largely by dint of being the first to really focus on building a database of these feeds.
As to format: virtually every podcast feed in existence is constant bitrate MP3 (confirmed by several different podcast directory maintainers), so this isn't really a concern. There are various technical reasons why historically podcasts have had to avoid VBR/other audio formats. CBR MP3 is guaranteed to playback without issue on almost anything, including your car stereo from 10 years ago.