As soon as you interact with the page, be it mouse, touch proximity, or keyboard, you could highlight clickable elements - perhaps with a border, perhaps links with an underline.
At least I posit 'a' solution! I'm not a fan of mystery meat navigation, and to be honest - there are plenty of sites - that use quite dumb non-intuitive UIs - including non obvious links and drop down menus. An intuitive navigational mode applied to web pages could really help.
I get what you are saying though. I'd envisage say, as soon as you tap the screen or move the mouse, all the navigational controls would be highlighted - rather than having to hover the mouse over something to see if it's a link or not.
As soon as you interact with the page, be it mouse, touch proximity, or keyboard, you could highlight clickable elements - perhaps with a border, perhaps links with an underline.
Then you have the best of both worlds.