Of course another path to take with this is to imagine that perhaps future tanks give up on the main gun as their primary tank killing weapon (say that after 120mm/125mm designers say enough is enough - we're not going to 140mm/152mm). Instead, in the LeoIII/Challenger 3/M1A3/T-XX etc the conventional gun becomes the secondary weapon (say something around the 50mm size) for dealing with secondary targets and that the primary anti-tank weapon becomes the ATGW. In this case, you end up with something more akin to a heavy IFV but without the troop carrying requirement. Maybe even akin to the CV-90 series?
One of the problems with that is chemical warheads are much more easily defended against than are kinetic energy ones, so at the moment armour is in the ascendency in the continual see-saw battle between protection and penetration. You would need to see a significant increase in penetration for chemical energy warheads. So, unless we see a change in the way such warheads presently work, this usually comes with a consummate increase in weight for the missile and it means the missile becomes large, unwieldy and expensive.
A way around that is to use a top-attack profile or the one I prefer, a high trajectory system such as FOG-M. Because they are attacking the thinnest armour sections on the opposing tank, smaller warheads or even more exotic systems such as EFP can be used. Both however come with their own difficulties and again, if reliant on chemical warheads can be defeated with reactive armour or active defence systems mounted on top of the tank.
One way around that is to use kinetic energy rounds - either missiles with sufficiently high velocities to mimic guns or guns themselves. We are though, now reaching as has been noted the limits with 120mm calibre and in the late 1980s NATO agreed to move to 140mm calibre, after the brief stint with a longer-barrelled 120mm smoothbore gun (L/44 IIRC). However such a large calibre carries problems with loading the rounds and so we have seen a move towards autoloaders. This in turn has introduced concerns about inadequate crew to perform routine tasks such as maintenance and piquette duty. Interestingly, the French overcame the problem by introducing "maintenance crews" into their armoured units and placed the now unemployed loaders in APCs to accompany the tanks.
Hypervelocity missiles have been flirted with by the US but they never reached any fruitition. LOSAT has come and gone, morphing into HATM, so obviously simply making a much faster missile is a little more difficult than one supposes. While it has the advantage of being recoilless, such a weapon needs to be fly a line-of-sight course, like a gun so they lose the advantage of being able to utilise full defilade which many normal missiles can.
The US FOG-M and the European Polyphen systems, utilising fibre-optic cable, rather than traditional wires for guidance are IMHO an excellent solution. They allow firing from full defilade, have no "gather" times and can even be utilised for immediate reconnaissance if necessary, utilising their TV cameras to report back on what is occurring on "the otherside of the hill" as Wellington termed it. However both have been abandoned unfortunately.