Even when you include training, the payoff period is not that long. Operational NWP is enormously expensive because high-resolution models run under soft real-time deadlines; having today's forecast tomorrow won't do you any good.
The bigger problem is that traditional models have decades of legacy behind them, and getting them to work on GPUs is nontrivial. That means that in a real way, AI model training and inference comes at the expense of traditional-NWP systems, and weather centres globally are having to strike new balances without a lot of certainty.
There's an interesting parallel to Formula One, where there are limits on the computational resources teams can use to design their cars, and where they can use an aerodynamic model that was previously trained to get pretty good outcomes with less compute use in the actual design phase.
Assuming you’re not throwing the whole thing out after one forecast, it is probably better to reduce runtime energy usage even if it means using more for one-time training.