I disagree - I think both are eminently "do-able" - the problem is between Peterborough and Doncaster they don't serve anywhere particularly large. And whilst the M1 does seem to 'shadow' the A1, the reality is it does so about 40 miles to the west (if you look at the distance of the A14 from Huntingdon to Catthorpe) - yes that narrows as you head further north - but from Peterborough for example, you're not going to head over to the M1 near Leicester to head north.
That's not to say the A1 is easy to upgrade - it isn't from Baldock going north, it's not too difficult until you reach Biggleswade where quite alot of work would be needed, but Biggleswade is growing, so there's a pretty good case for upgrading the A1 and eliminating the roundabouts on it where there is 'east-west' traffic vying with 'north-south' traffic. Biggleswade - Sandy, the challenges are Lower Caldecote and Beeston. Now the Caldecote area has been touted for large scale housing on a few occasions - so maybe that will provide the opportunity to sort out the A1 - Beeston's trickier but a further bypass of Sandy to the west (can't do to the east because of the nature reserve) might be the solution there. Next you've got Tempsford where again a load of housing is planned, plus east-west railway, so that's a good opportunity to sort the A1 and get rid of that absurdly dangerous entrance into a boat yard which for the benefit of those who aren't familiar with it is from the *right hand lane* of the northbound carriageway. After that you've got a couple of villages which are probably easily sorted and then you're at the A1M at Alconbury.
I don’t doubt that it’s feasible, but I think it would stall at the political stage. Probably a classic case of people wanting the improved road, but not wanting the disruption that would come with delivering it, especially as there would likely have to be some amount of property acquisition.
It’s already very conspicuous that the five remaining roundabouts between London and Berwick are all on the Baldock to Huntingdon section, and whilst Black Cat now seems like it’s finally going to go, I don’t think there’s any real plans for the remainder. We can’t even get the S-bend south of Buckden smoothed out, and there’s still plenty of at-grade junctions on this section as well.
The Home Counties never seem to be a priority for this sort of thing, the politicians seem much happier providing gold-plated A1(M) in North Yorkshire!
If I were spending money I’d sort the roundabouts at the southern end and do a few small schemes to get rid of the worst flat junctions, and I’d do motorway on the Doncaster to Ferrybridge section (which I always find is generally the worst part of a journey up the A1 due to the very high number of HGVs). If there was still money to spend then next priority would eliminating as many flat junctions as possible between Peterborough and Doncaster.
Oh and 3 lanes plus a hard shoulder between Welwyn and Stevenage, but I’m resigned to never seeing that in my lifetime!