It really depends. The problem is that once advertising become the primary drip of financial resources, the content begins to revolve around the needs, goals, and preferences of advertisers. Content that isn't seen as monetizable gets shown the door. Content that rails against consensus opinion or is anti-corporate gets shut down. Things that earn money get promoted at the expense of all else.
You can see this lucidly in the case of Bill O'Reilly. People had already known his deal for over a decade, but it wasn't until his ad dollars were pulled (after a public pressure campaign) that he was dethroned. That's an example of the kind of media system that is fostered by advertisement.
Hasn't advertising always been the primary drip of financial resources for podcasts? Aside from a bit more enthusiasm for Casper mattresses than is probably warranted, I don't think your concerns have come to pass.
The great thing that podcasts have going for them as a product is they're super cheap to make (relatively speaking). Podcasters willing to compromise the product by taking on more obtrusive advertising will get outcompeted by those who don't. It's ideally how media sites in general would work, but those are expensive enough to run that most sites resort to intrusive ads.
You can see this lucidly in the case of Bill O'Reilly. People had already known his deal for over a decade, but it wasn't until his ad dollars were pulled (after a public pressure campaign) that he was dethroned. That's an example of the kind of media system that is fostered by advertisement.
EDIT: changed 'decades' to 'over a decade'. https://www.rollingstone.com/politics/features/a-timeline-of...