The type of radiant hydronic now used is not your standard slant fin radiator......
Once the concept of thermal storage is introduced, standby heat is less critical as the house may be able to go for a day or two off of thermal storage. If electric heat it needed, the utility can easily signal the backup to turn off during peaking events which are normally at worse a few hours. My area is now requiring home sprinklers inn new and retrofit construction and in most cases that requires a big tank of water in the basement for reserve storage for the sprinklers so the next step is use the thermal storage for the sprinkler storage
I have to agree that thermal storage is a nice feature of a hydronic system in a way that is not feasible with forced air (big box of dusty rocks anyone?).
One could certainly imagine that integrating hydronic storage with a PV powered ASHP running right into the hydronic store would be sensible. The PV and the ASHP would both work during the warmest parts of the day, and no battery (or a minimal one for hour-scale buffering) would be required. In a future world where seasonal electricity load costs are passed to the consumer (so a kWh in New England is more expensive in the winter, and cheap during the summer), which is one in which net metering of rooftop solar is obsolete btw, you could imagine that such a system could be appealing.
Nerd alert: I already think about banking cheap BTUs, bumping my thermostat/ASHP mid-day during warm spring days, and getting the heat back at night when I do a setback. I wish someone could build a smart stat that could do THAT automatically using the weather forecast temps my Ecobee already has on board. A hydronic HP + storage system would be this on steroids, with constant service temp bc you wouldn't be living in your storage.
I'm also down with Euro-style hydronic radiation in a super-insulated house (or multi-unit apt building with a central heat supply). With smart controls you could certainly have a controller that knows both the outside temp (load) and the (perhaps changing) temp of the hydronic fluid (supply) and radiation curve to have a nice steady balance.
I guess I have two feelings about this... From a strictly engineering point of view, there is certainly a lot of cool/eff/comfortable things one CAN do with HP-fed hydronics, that have a place in a future electrified HVAC world. But on the other hand, I think in the long run legacy buildings will get upgraded/replaced with what we would consider super-insulated stock. If the grid operators of the future manage to find a solution for the seasonal storage problem (i.e. HVDC lines) then most homeowners will not want to pay for the complexity of a hydronic system with massive storage, just bc it will eat into their square footage!
Analogy: I think houses are where we were at with cars around 1985. We saw another 20 years of ICE tech improvements, with an impressive improvement in MPG (and peak HP) but at the expense of complexity and cost. And in the end much of it will be replaced with MUCH simpler and cheaper EV drivetrains.
For example, Passive houses were mentioned upthread, with HRVs. IIRC the originators pointed out that HVAC BTUs could be distributed trivially via the same ducting used to deliver fresh air, and that simplification was a goal and a feature early on. Why do I want to have a ton of (even spiffy Euro style) radiation if a 2-3" duct and return to every room keeps me perfectly comfortable? Answer: in climates where that is possible, forced air will reign supreme, in colder climates advanced hydronics will remain.