How would the economics change if we could only communicate at light speed, but had a functional Alcubierre drive (or other lightspeed technology) and could travel at FTL speeds?
Tapes have mass. Unless we learn to suppress inertia, it would be easier to encase the message photons in an Alcubièrre field.
FTL === back in time, and maybe we don’t observe it since it doesn’t happen often. Like in iPhones that don’t spontaneously in cosmos every 2^30 years. Another cue is QM entanglement that somehow resolves the inconsistencies by out-of-timeline ‘decisions’ of what ‘really’ happened once you checked the outcome. If nature works in mysterious ways, why couldn’t it resolve the fact of time travel by the same logic: yeah, an object appeared from nowhere, but it disappeared from somewhere, no brainer. Our puzzle is to create serious enough paradox for the nature for it to resolve it in a desired way. First experiments may resemble our first ‘friendship’ with the energy of atom, but then who knows.
Being able to travel faster than light, or send messages faster than light, would not involve objects popping in and out of existence. That's not even a particularly well-formed concept. You and everything else you know are already moving through time and space, and the rules for how that happens also suggest that if you bend the geometry of the universe sufficiently, you can move to a place in less time than it would take for light to cross it. If you then return, you can end up arriving at your origin before you left it. Relativity does not allow the universe to spontaneously warp itself into the kind of pretzel which would allow for things to travel instantaneously back in time, and if it did, the effects on anything else nearby would likely be catastrophic beyond ready imagination.
Much of your speculation is rooted in misunderstanding. It's more difficult to explain things because your conceptions don't map well to the actual physics. There's a series on YouTube by PBS called Space Time, which I would strongly recommend as an accessible guide to relativity and physics in general.
Unfortunately so to my imagination. But I still hope that there is many orders of magnitude more quirks that could obsolete current well-proven models and open the world of possibilities. Honestly, modern physics restrictions are boring to death.