This is a familiar story of bypasses and newly re-routed major roads which cross the lines of pre-existing rights of way without 'obstructing' or 'blocking' them, leaving them 'accessible' via stiles or sometimes steps (as here) and sometimes (but not always) gaps in the central reservation (so that's all right then). Local examples: a wet underfoot and hence often overgrown path alongside and then straight across the 60mph plus A629 dual carriageway near the Steeton-Silsden roundabout (which does not [yet] have a footbridge or subway). This one isn't a named 'Way', not that carrying a moniker would make much difference. Another is the path north out of Skipton from Corn Mill, which is a great route (and part of more than one Way) but goes across the bypass. Its near neighbour does the same, this time down rather then up, but there's an alternative via a minor road bridge (and then down some steep steps to an often overgrown wallside path to a stile, into also usually wet ground.)
Do we expect every existing right of way to have a subway or footbridge over every bypass or main road ? In the above cases, the first is horrendous and only once attempted by me (but may soon have a near alternative), the second is ok (I'll be leading a walk across it in August), and the third could have merited a footbridge but the nearby minor road is better. The Pennine Way's famous footbridge over the M62 is an excellent example of how it should be, but when the motorway was constructed the PW was the most walked route in the UK. There are now so many 'named' routes that merely rebranding an ancient footpath as a 'Way' carries little guarantee that it will be accessible, safe (LOL) and clear of under- and over-growth. Yesterday I negotiated a brambled and nettled hedge in south Derbyshire with a hidden and high-drop stile, after asking the locals if that path was 'overgrown' - but it did have a good footbridge over a waterhole, so of course it was 'accessible'. (I had been on minor roads because of hayfever and as yet uncut fields, just tried this one because it was a good shortcut on a very hot day.)
It's a problem of too many rights of way versus new roads and developments for them all to be rendered properly usable. The boom in outdoors activity may encourage local councils to put more resources into footpaths and bridleways, but that would be optimistic. When there were resources for such things (pre-2008, pre-Covid) there were many new named routes, some with fingerposts and leaflets, now out of print and out of maintenance budgets. It's a lottery, the only to way to find out if a bit of path is doable is to try it, sometimes it's a learning experience but more often, surprisingly, you can get through, maybe scratched, stung and annoyed, to the next one. If you're attempting a little-known but named Way for the first time there will often be people here and on the Facebook site who can offer advice, particularly safe alternatives to major road crossings. Just don't try the A629 path near the Steeton-Silsden roundabout.
Iain