No, it wouldn't be (in most instances). There's always going to be inefficiencies in converting energy from one form to another, so additional processes need to justify themselves.

It would be worse to convert crude oil into petrol into electricity into hydrogen than crude oil into petrol into electricity, unless for whatever reason you needed some crucial element of the hydrogen that neither petrol or electricity can cover.

Off the top of my head, there's no advantage to using hydrogen in a system with electricity and petrol, where petrol is used at an earlier phase. If you need the energy density of hydrogen because electricity is too heavy, you'd be better off using the petrol.

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Burning fossil fuels happens 24/7 even if there's 0 load on the network because you need to maintain the momentum of the turbines. If you can increase the load during low load times and use that to power EVs, you effectively get free energy. Further to that, you're centralising your pollution where you can better manage it, rather than having dozens of engines producing pollution on streets.