Forgetting the part that we would need literally an infinite amount of energy to get to the speed of light in the first place, time would stand still for someone travelling at the speed of light. So from the traveller's point of view, they'll arrive at their destination at the very moment they hit the speed of light.
Is an infinite amount of energy truly needed or is that just an 'illusion' from the viewpoint of bystanders? If so then the math itself is also based on the viewpoint of bystanders. If TIME itself ceases when an object hits the speed of light, bystanders will see it blasting through space, but as you pointed out, when arriving their destination it is the instant they hit the speed of light for them. When hitting the speed of light, does the energy also cease to age or be consumed? If that's the case, then it's only the energy to approach and get close to the speed of light and there should be an adjustment for time dilation. The only easy way I can think to explain this concept would be if you were to build a fire and must heat it to 10,000 degrees and make it last for 5 years. Imagine degrees is speed and years is light years. If the energy is measured at 10,000 degrees and lasting 5 years, vs if it hits 10,000 degrees and the 5 years is instant since time stopped for it (thought from our perspective it's lasting for 5 years).
Not sure if this is considered when saying needing infinite energy to reach light speed or if this concept was not considered when those theories were made.