It would be a means to balance the Power Armor out while allowing it to be used when you like.
We don't know how it would work later because we haven't seen late-game power armor, it is entirely possible that there is an upgrade that increases the core capacity. Like the jetpack seems to be an upgrade as well.
We also, as mentioned, don't know how much energy it consumes. You're worried about "constantly refueling" when during that snippet it barely went down. No idea how long you can go on a full Core, and no idea how much a full Core takes. It might be entirely possible it's fueled by Energy Cells, which as an ammo you can carry abundantly.
Sure it could in theory just be to power the flashlight, but do you honestly believe that? They're going to give you an infinite energy Power Armor, but it can't keep its headlight on? Which isn't a problem for the little pip boy somehow... Seems highly unlikely.
The Power Armor already has it's Health. Seems redundant to add double cost, one being the health of modules that need to be repaired and the other being energy.
Also lore wise i am not wrong. What you find is the most common model of Power Armor, the T-45d model. Which uses Small Energy Cells as fuel, SEC are also an ammo type, and burned through it an alarming rate. It was the newer model of Power Armor that came with an "infinite" microfusion energy pack.
Just google T-45d and check it's back design and compare that to the Power Armor of Fallout 4, it's practically identical.
edit
Scratch that, upon closer inspection it seems its the T-60 armor you find in Fallout 4. It runs on Microfusion Cells, and it still seems looking at the Core in the HUD that it drains energy on use and not damage taken. Taking damage, even big hits from a Deathclaw, don't reduce the Core but instead show up on the left in the visual representation of the PA, where damage parts turn red or disapear.
It's a bit confusing to make it out from the gameplay trailer because they used several different playthroughs of that bit with the Power, cut and pasted pieces of each playthrough to make the montage we see.
The number under Core in digital seems to read 11. I'm just guessing, but maybe thats the number of Microfusion Cells you have.