[Ethereum] Why don’t private blockchain networks that do not charge for transactions charge a fee when processing ethereum/ proprietary token on the network

The public network charges for transactions which make it popular with the public.

It's more complicated than this. Charging for transactions creates an incentive structure for miners. In a public system, where trust between transacting parties doesn't exist, cryptoeconomics comes into play.

The private network does not charge for transactions which is why it is popular with businesses.

It's more complicated than this. The trust model is different, and cryptoeconomics plays a much less important role.

Why is there no network that can do both?

Lots of people use Ethereum privately. Further, lots of people set up their private Ethereum network to run without transaction fees, which can be done by tweaking the code. I'd assume similar things can be done with the codebases of other other blockchains.

But that's missing the point: these are two completely different use cases, to the point where you could claim that "blockchain" technology itself makes less sense for private business networks. Which is where the Digital Leger Technology (DLT) vs. "blockchain" comparison comes in.

See: Blockchain vs. Digital Ledger Technologies (external Consensys link)

For example eosio | Blockchain software architecture is trying to make it cheaper to process transactions which I assume is meant to appeal to businesses and consumers.

At the cost of security. EOS uses a Delegated Proof of Stake consensus mechanism, which increases transaction throughput at the expense of decentralisation. This is like possible with businesses, who own their entire private network, and thus can guarantee security. But popular with customers on a public network? That would depend who you ask.

Why cannot a private blockchain such as Hyperledger Sawtooth/ Fabric which are private be free for businesses to use because businesses validate transactions but also accept a token which has value and when a consumer users the token to purchase an item from a business in the network either charge a fee for validating the transaction or do not charge for it.

It's not entirely clear what you're asking, but it sounds like you're wanting to create interactions between a private network and a public network, which would require some complicated economic/cryptoeconomic design to work.