My data, is old but...
I went to the base of Mt Everest on the Tibetan side in 1987 in a "gypsy cab", a 1950s vintage Land Rover. It was doable even then, although it involved very rough travel over several 18,000 foot passes, and several deep-river crossings (no bridges in the Rongbuk Valley, at least then).
There was a rough cart-track from the main Lhasa-Kathmandu highway (which itself wasn't much of a highway then). There was, however, a steady stream of Land Cruiser traffic even then -- several vehicles loaded with "tourists" a day, at least. I know this because at one point, we became hopeless mired in the river for a day-plus, so we got to know the locals in one village very well. Back then, only the (fool)hardy stayed the night up at Rongbuk or anywhere up the valley, so most of those trucks were one-day turn-arounds. We did spend the night at Rongbuk Monastery, and it was an amazing experience all around, but certainly not for the feint of heart or weak of lung.
MichaelJ, the altitude change from the Lhasa highway to Rongbuk Monastery was on the order of 3,000 feet, though again, you had to go up over at least one 18,000 foot pass after you left the main highway. From Rongbuk Monastery, it was another mile or so (though not a lot of elevation gain) to the bottom of the Rongbuk Glacier, which is the location of the Tibetan-side base camp.
Even given modern China's propensity for huge public works projects, I don't think I would expect a Chinese interstate highway any time soon. My guess (not data-based) is that they'd be 'improving' the cart-track and adding bridge crossings, which based on my experience, at least, are crucial for safety. The actual "roadbed" in 1987 was essentially an opportunistic trail along the riverbed and threaded along through several small villages of a handful of houses. The route over the mountain pass was similarly opportunistic, and kind of clung to the ridge with a staggering number of switchbacks. Yaks make fair road engineers, as it turns out.
<OK, now I have read the CBN link which I should have done first. Blacktop. Undulating guardrails. Yikes. Gonna be a powerful stack of altitude-sick sunburned white people up there. We brought down a well-prepared, healthy trekker with moderate edema when we left Rongbuk. He probably would have died if we hadn't. Notwithstanding how I feel about the Chinese treatment of the Tibetans -- not good -- this is really a bad idea from a "tourism" perspective.>
