There are hundreds of thousands of junctions in the UK. 10s of projects does not make any significant difference.
Sure they do. Some junctions carry several orders of magnitude more than others.
And for the kind of money we're talking about for HS2, you could do a lot more than 10s of these projects. The entire A14 upgrade through Cambridgeshire -- a single project spanning many miles of a major trunk route -- only has an estimated budget in the region of £1B, about 2% of HS2, and this is work that has been delayed for years because of the cost despite a crazy number of accidents, many of them fatal, happening on the existing A14 corridor every year.
I figured that's what you were doing. Yet local roads are significant. Few journeys start and end by a motorway or dual-carriageway.
No they don't. But again different roads carry vastly different volumes of traffic. When the M25 was effectively closed a few days ago because an overnight repair didn't set properly, there were 16 miles of tailbacks, across 3-4 lanes, for several hours. That is roughly equivalent to gridlocking an entire small city for an entire working day.
And what of the M4 bus lane scheme, where it was deemed that using fewer lanes for cars actually speeded up the cars journeys?
You go with the evidence, of course. I'm not saying building more roads is always the answer to congestion or inefficiency in the road network. On the contrary, as I wrote before, traffic engineering is sometimes a surprising field with counter-intuitive results.
My point throughout this discussion is simply that high speed rail is in many senses a very expensive type of infrastructure to build, and there are certainly alternative uses for those resources that might plausibly give much better returns. Improving the road network is merely one possibility, and as you just demonstrated, there are useful improvements that can be made that don't necessarily involve building new roads.