Yeah, that's still an issue. Except...you're running your laundry on a timer now.
The models you listed on that link do not have start timers. Electronic controls, yes; but without timers, all that means is you can't mechanically set a setting, and then have a timer power the thing on at a specific time. Nor do they have protocol based external management, so you could trigger them at a particular solar generating level that's sustained over a period of time to avoid using grid power, and program a (much smarter) external system to run them.
These appliances are not as smart as they'd need to be, and even if they are, they're not smart in the right direction, nor are the external control management systems there yet for doing things like coordinating the dishwasher vs. the laundry.
Just have it set to run twice each week on different days instead of twice in one day, back-to-back.
Dude or dudette, I totally promise not to tell your SO that you just put their favorite yellow shorts that they've had since college in with your new blue shirt and turned them green. But you *will* be buying them that expensive dinner by way of apology.
Us laundry ninjas know you can't just throw in anything with anything else. Some things will simply shred if you put them in with some other things, like delicates and thick towels, instead of putting them on a different cycle. What this boils down to is that any given laundry day requires multiple loads.
Put in the next load before you go to work, take the dry clothes out when you get home, no problem.
And forget this, if you have kids: there's no such thing as a small amount of laundry, or two day a week laundry.
Look, personally, I want local energy storage: I don't want to have to change everything, just because I'm going to be powering everything with the big fusion reactor up in the sky, instead of the little fission reactor down the coast. At some point, it becomes a quality of life issue, and that point hits pretty hard with solar in a different way.
As soon as there's enough solar capacity, and people aren't home to use it, then it redefined "off peak" and "on peak". The "off peak" hours are during the day, when generating capacity exceeds demand, and the "on peak" hours are during the morning and evening, when you're at home and awake, but the sun isn't shining, so there's more demand on the grid, because everyone else keeps the same hours you do.
One of the reasons the PUC in Nevada got rid of net metering was because Nevada was on a trajectory to eventually hit this "solar tipping point", and it was obvious to the utility company that at that point, they'd be paying spot market prices for energy, mostly in the evenings, and they'd end up pretty screwed.
Unless I can have local storage, and it's got to be able to store everything I can generate all day, assuming it starts out dry, the "grid battery" approach looks to be doomed to jacking my utility bills right back to where they used to be, so the power company can maintain revenue under the pretense of "we have to maintain the grid, but all these people have solar, and aren't paying us enough for us to be able to afford to maintain it".
The only viable alternative is to be able to pull the plug completely. And sadly, solar is just not there yet.