There is - you make the thing unaffordable as the land take required for bridges to gain height etc is too great and the political will drops off the cliff. AAR plate H is 2m taller than W12/GB+, which you will notice when you need to pass under any bridge along the route.
Surely most of the time new routes tend to go over the old ones, rather than under, because it is dramatically easier to build an overbridge without mass disruption to the other route than an underbridge. I'm skeptical digging an underpass a metre or two deeper will have that big an impact on cost given the availability of Werrington style boxes (or the Alameda corridor in the US) that have land take largely decoupled from depth of the cutting.
And in tunnels engineering constraints related to evacuation walkways for train crew and the circular nature of most modern tunnels (dug by TBMs) will force quite a large height anyway. Even tube-gauge tunnels have reached 5.2m diameter on the new construction!
Given the trend in recent years across the west has been for ever greater fractions of lines to be built in tunnel - I'm not sure adding an extra 1.5m over the HS2-style GC gauge is going to matter too much.
Note that the one route built new for freight in Europe in recent years (the Betuweroute) was built with structural clearances for double stack operations, albeit not with operational clearances to avoid modifying pantographs on rolling stock for greater travel and because none of the connecting infrastructure could do that.