"I think you'd agree that there IS a need to get it fixed as soon as poss"

Yes, but not at ANY cost in terms of damage. To clarify (based on what they say, not my speculation):

"Doing nothing" is indeed the worst and most damaging option. Ergo, doing "something" (even tunnelling) is preferable, I agree.

However, it's not that simple. The "doing nothing" damage has been speculated to take a very long time to fully work itself out. They've suggested parameters of 300 or 1000 years, depending on the nature of the collapses, but they don't know which will apply. They've also suggested lower and upper limits to the amount of possible damage.

On the basis of their figures, you could speculate the comparison as follows:
Grouting tomorrow = 13 cubic metres of loss.
Tunnel tomorrow = 166 cubic metres of loss.
Do nowt for 1 year = between 2.5 and 4 cubic metres of natural loss.
(Though, natural loss may not be "smooth" over time - it could be a series of random collapses - they haven't said).

If you keep those figures firmly in mind, any press release that gives the impression that EH must go in there on white chargers and tunnel to prevent ongoing damage begins to look a little silly.

So I'd agree "there IS a need to get it fixed as soon as poss" but NOT necessarily by a means that imposes perhaps 66 years worth of natural damage on it!

But what do I know? I've probably got hold of the wrong end of the stick from their figures, and they don't say that at all. So ALL that's required is expert confirmation that I've got it entirely wrong.