No chance of a Hitchin (or Stevenage) to Luton link - it's totally unnecessary and would be across Green Belt land which is undeveloped. Also the MML south of Bedford is full to capacity - there aren't any additional paths to force E-W services along.
A far better idea, which would need minimal infrastructure work, would be to send them north from Bedford to Corby and then with a curve at Manton on to Stamford and Peterborough.
Peterborough makes FAR more sense than Cambridge as the ultimate destination - it's on the ECML for both suburban and inter-city services, there are links to most of East Anglia, Lincs and the East Mids.
I'm not advocating EWR goes via Luton - far from it, I think the idea is madness for precisely the reasons you suggest.
The problem with all the schemes is that they don't serve Bedford Midland properly for interchanges, or the only option that does (running to Peterborough), goes so far around the houses so as to be unviable.
I propose heading through Bedford Midland, swinging east around the northern edge of Bedford and heading for St. Neots. It's halfway between Stevenage and Peterborough, and a reasonably-size population centre in it's own right, and has open land alongside the railway - perfect for the ECML interchange. From there head east as more new build via Cambourne to Histon and then down the former St. Ives branch (the MGB can use the roads - that's it's primary benefit, right?
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...I do think there is a good case for Luton to Hitchin though - but ideally as a line from Dunstable. It would be able to serve Luton Airport directly, enabling you to close the parkway (speeding up MML services). You're not even forcing passengers to make an extra change - they already have to change to the bus at the parkway anyway, but it enables a proper rail link. Rather than restore to Leighton Buzzard though I'd send it down to meet the WCML at Cheddington and use the old route to get to Aylesbury. You could then conceivably get down to Princes Risborough from there, and a reopened link to Bourne End gets you to the GWML....and a few more changes might make reaching Reading viable, giving you some kind of strange loop service between Reading and Cambridge.
All rather fanciful, but it'd be one hell of a handy network.