You get your ability to cast arcane spells back by resting through the mental rest, because of the mental focus required to shape those external energies. It takes a lot of willpower and focus to cast arcane spells, the mental rest and recuperation is what is important.
The idea that arcane magic comes from within is so absurd and breaks so much established D&D lore that it's not worth even giving serious thought to, it is to be dismissed out of hand as inherently ridiculous. Sorcerers have an innate talent for directing and channeling magical energy, but it's not from within them. Whoever wrote fluff saying otherwise, quite bluntly, was creating major contradictions in the lore.
You forget the "in my opinion" part of that. Because, I have often seen in the text and various sources, about people being tested for "magical aptitude" before being allowed to study magic. Or with them discovering a "latent power" that allows them to cast magic. In many of the DnD novels magic is described as an internal force.
Also, see what you did there? What does it take to cast spells? "because of the mental focus required to shape those external energies. It takes a lot of willpower and focus to cast arcane spells". Sounds a lot like... psionics. Intense mental focus and willpower.
Or, to put it in specific examples from the lore that specifies that it is not internal and is ambient in the world.
If magic came from within, in Forgotten Realms, the death of Mystryl due to Karsus's Folly wouldn't have caused magic to go wild then fade for several minutes, and the death of Mystra wouldn't have caused the Spellplague. In Dragonlance, the loss of the 3 Gods of Magic, and their gift to the world in the form of arcane magic, in the time between the Chaos War and the War of Souls wouldn't mean that Arcane magic was lost to the world and they had to discover a completely new form of magic in that time that didn't even fit D&D forms of magic to the point that TSR used a non-D&D game system to represent that era, that or they had to find old magic items and plunder them for the magical energies trapped in them as the last remnants of Arcane magic in the world.
That's 2 of the major D&D settings that would have major world-sweeping metaplot events (2 in FR, 1 in Dragonlance) that just plain wouldn't work if Arcane magic worked like you described.
Sure it could. Fairly easily.
Let me ask you a question, what would happen if the diety in charge of defining air and its movement was killed? Would the air inside your body work the same way?
Because there is air outside and inside your body. At the same time. You can't talk or sing if you have no air inside your body, and you can't tale or sing if there is no air outside your body.
Thus I see magic. Both internal and external. Because if it were purely external, then spell slots wouldn't be a thing. I would be like a Warlock. I can cast five spells, total, not three 3rd level, one second and a first level. The levels of slots must represent an internal reserve of energy, not the mental focus of moving external energy.