It’s exactly the same consents process, with the same requirement to demonstrate you have considered options, requiring a similar level of work. All it would remove is the time and effort of responding to certain specific objectors. In the scheme of things this is a relatively small cost.
Whilst it is true that it is technically the same process, what you are proposing does have some bearing on the cost and difficulty of the consultation, both in cash and political terms.
Which is why HS2 has a giant tunnel under the Chilterns, even though it would likely have been substantially cheaper, in cash terms, to cross the region on the surface. Indeed I'm pretty sure the cash optimised route over the Chilterns would have no tunnels at all.
Every infrastructure system requires both money and political capital to push through.
I've simply come to the conclusion that political capital is now considerably more valuable than money.
And as
@Ianno87 says, you’d still need ventilation shafts / escape shafts / headhouses every couple of kilometres as well.
Surely the quantity of surface infrastructure would be entirely dependent on the engineering choices made in the tunnel's construction?
After all you could reach Bedford to Sandy in a length that technically allows for only one surface shaft, using the example of the Ceneri Base Tunnel, or no shaft at all, from the requirements of the TSIs.
But I will stop at the risk of derailing the thread.
EDIT:
Maybe it's just my nuclear background colouring my perspective!