The answer is obvious, you synthesize hydrocarbons. It's your guess as to why this isn't done or hardly even talked about.
The maximum power you can take from the grid depends on the max. power of your electrolysers. But you only want to run the electrolysers, when they are profitable, that is when the electricity prices are low enough due to oversupply. On the other hand the whole equipment is probably expensive to buy and keep running, so you want to run them as long and often as possible. Additionally you may use energy storage to prolong the profitable time windows of your electrolysers.
That said, it would be really great, if hydrogen and/or hydrocarbons would be synthesised at scale. There are many pilot projects and I hope one finds the right tech and trade offs to make this profitable.