If the ads are being added by the content creator and you don't like that, the solution is to not watch that content creator, not blame a random streaming platform for supplying unadulterated content.
Spotify could require that content creators upload ad-free versions of their podcasts for premium users. This would probably require a significantly higher subscription fee to support much larger payments to the podcast creators.
Podcasts are generally accessed as a syndication service. Except for ones actually contracted by Spotify, like Joe Rogan, they are just importing them from RSS like everyone else.