The current estimates for "green hydrogen" are $5/Kg. The DOE goal is to try to get that down below $1/Kg, although it probably needs to get down to $0.50/Kg to compete effectively with natural gas. The picture gets further complicated by location. Rooftop solar in New England has an 11% capacity factor. It is worse in the winter. Recently, in CT, we had night time temperatures in the single digits for several days with more forecast in the next week or two. With daylight hours shortened due to it being winter time, sun position being low on the horizon, and partly cloudy conditions on most days, there is not enough power delivered by the solar panels to electrically heat the house 24/7 including the use of batteries. Generating hydrogen locally will not produce enough hydrogen to get through a cold night, never mind several days of cloudy weather. Of course, the hydrogen can be generated elsewhere and delivered to the home for energy storage at the home with sufficient capacity to overcome this, but I didn't get that impression from the brief description.
Hydrogen is being considered for energy storage for precisely the reasons that I mentioned (longer duration intermittency). MIT studies have indicated that batteries by themselves will not likely be sufficient to handle multiple days without sunlight or wind. They note that little or no wind can last for up to two weeks, while cloudy days can last for about 1 week. During that time, batteries will be depleted and not able to recharge if there are no fossil fuels being used on the grid. Current batteries can operate for up to 4 hours and are fairly expensive. Therefore, multiple batteries would be needed along with the extra capacity needed to charge those batteries. Fuel, on the other hand, can be generated separately and stored for long periods of time. Thus, seasonal swings as well as shorter term needs can be addressed. That is why storable fuels (like oil and coal) are so useful.
The other point to be made is that of costs coming down. I am less certain of that, particularly in view of the inflation that we are now experiencing. Of course, no one really knows what inflation will be next year or next decade. However, raw materials costs, particularly copper and semiconductors, are going up substantially. Shipping costs and labor costs are also increasing. Solar panels only represent 10 - 15% of the cost of an installation. The disinflation that we have seen for the past 40 years may, in fact, be over. That does not bode well for the assumption that costs will continue to come down. They might, on a relative basis, but, then again, they might not. A lot more work needs to be done.
Hydrogen will likely have its place, but it is not the "silver bullet". A combination of technologies including nuclear, renewables, fossil fuels with CCS, improved efficiency, batteries, and others yet to be developed will be needed.