For me it shoots the host's credibility.
For me, this is it in a nutshell. I understand the need for ads to support the broadcast, and most of them don't bother me because I don't listen to the kinds of shows that would advertise fake medicine, and my podcast software lets me jump ahead or back 30 seconds at a time, so I mostly skip over the ads.
But in the realm of questionable personal endorsements, one of my favorite podcasts is one of the worst offenders: Sawbones. I love the show. But the way they pander to their advertisers is unsettling.
At the opposite extreme, as mentioned already, one of the best is Oh No, Ross and Carrie, whose tone makes the ads fun to listen to.
There's a big difference between going on and on for minutes about how this is the best (mattress, underwear, brokerage, etc.) in the world, and just saying These folks sponsor us, please support them. As Devout says, it's a matter of credibility. In a podcast that purports to provide information, credibility is important. In one that's purely entertainment, credibility is less of an issue.