Interesting thought experiment but practically unworkable.
Product placements are a one-time thing and a tv show isn't shown once but hundreds or thousands of times across different geographical regions and accross time (there are still shows from the 60s being aired).
On the other hand, TV commercials are very time and place dependant; maybe Coca Cola can afford an ad on national tv but a local station is more likely to show an ad for a local furniture company -and get revenues from that ad.
Relying only on product placement and asking the distributor of the show to pay for it to be aired would require product placement to be massively expensive as it would need to pay for national and all local tv stations costs.
The nature of advertisement makes it valuable mostly for limited amount of time and to a limited target audience. That makes sponsors less likely to be able bear the huge cost of product placement relative to the impact that placement can have.
This idea also means that TV stations would only be able to air a very limited set of shows: those that can afford to pay them, meaning that most local stations would not be able to show anything, either because they are too big and expensive, or too small and don't have a suitable target audience for the show's embedded advertisement.
On top of that, it would require tv shows to raise massive amounts of cash to be able to afford to be aired. This would kill any small production and we would end up with large corporations basically having to optimise the shows for their advertisement potential as they wouldn't survive otherwise. We're just going to end-up with shows that will be little more than hour-long commercials instead...
Frankly, in what way is any of that an advantage over the current crappy situation?