Having to make a decision about whether to tip/donate to what would rapidly become nearly every site on the Internet would be a terrible user experience. "Decision energy" (aka willpower) is a scarce human resource; this would be an unparalleled waste of it.
I wish there were a great alternative to ads as well, but I believe action-required micropayments will always be a non-starter. The best we've got so far are tools like Patreon and Bountysource's similar system. These can be viewed as a kind of "preaggregated micropayments", which eliminate per-click decision making via a user-configurable subscription.
> the browser might "protect" monetized pages in some way
It's already possible to disable copy on web pages. Some blog themes do this, and I wish browsers would just unimplement it entirely. This is right up there with lame DRM schemes, in that view source (or else curl) are still going to work. Likewise, bots will be completely unaffected. Such an approach merely annoys users with legitimate needs (e.g. who must to look up a word or phrase), but will have zero impact on content piracy.