I know where you are coming from, and I myself would prefer something of this sort rather than the ad-choked pages _or_ the paywalls of today.
That said, paying _anything_ at all - even a fraction of a cent, is a problem for a very large portion of humanity.
* Poverty is one part of it. In India, the ARPU - Average Revenue Per User - of mobile providers is less than 2 USD/month. There are literally hundreds of millions of people who do have some sort of data access on their cheap android phones but cannot afford to spend even 10s of cents over and above their data charges. Its taking all our effort to get information services to them as cheaply as possible.
* Payment method - billions of people around the world do not have a method of making a payment online. No credit cards, no (usable) bank accounts. India is trying to get every adult a basic bank account, theres been some success there, but these are people who do not even have the equivalent of 2 USD to deposit in their govt provided free bank accounts.
* Regulatory hurdles - for the longest time, making a dollar payment from India involved running to the "foreign exchange branch" of your bank in the closest large city, filling out forms in triplicate, explaining why you needed the dollars, getting approvals, and then being issued a cashiers cheque for the exact amount already made out in the name of the recipient. This is no longer the case, but currency controls are part of most economies even today, and become tighter during economic crises. Any kind of mandatory payment would function way better than the Great Firewall in keeping people out. Such payments would also result in a massive privacy violation, because payment processors will want to keep a log of each transaction (sender, receiver, amount) pretty much forever, instantly killing any privacy benefits of TOR, VPNs, etc.
Yes, its possible to offer both, in theory. What would happen is either the micropayments would work or they won't. If they do, a very large number of sites will prefer going pay-only (like the WSJ) rather than deal with the nastiness of ads. If they don't, we are anyway back to where we started.
For some sites, it works I suppose - I know some forums offer a "subscriber mode" with benefits including ad-free versions. That is reasonable to an extent. But for a very large proportion of sites its not reasonable to go that way.