I'm gonna assume this is your first floor tiling project.

It's all the practical considerations that you're overlooking that would make such an installation method unworkable. Wire comes on a spool. It's going to want to curl, even between your staples. That wire is going to make troweling your thin set onto your tile backer a problem. And, when you use the cable tie to pull the tile down taught, you're most likely just gonna pull the wire up rather than the tile down. AND, with all the extra work you're doing, and the additional time that takes, your thin set is going to skin over so that it doesn't wet the back of the tiles you're setting, and your tiles won't be held down well.

I've yet to set my first floor tile, but I've done way more than my fair share of wall tiling. What you'll find when you set your tile in thinset is that it'll easily push into the wet thin set up to a certain point, and then the tile will want to stop. Pushing it any deeper into that thin set becomes very difficult once the tile wants to stop.

So, instead of your wire/cable tie/dowel idea, what I'd do is simply trowel the thin set down on your tile backer board holding the trowel at a comfortable angle so that your thin set is of uniform thickness. Then push each tile down until you feel that sudden increase in resistance to further movement. Then, press down with the edge of a spare tile ACROSS the two grout joints between previously set tiles and the tile you just finished setting.

Or, at least that's what I do when I set wall tiles with thin set.

Why not just buy a sheet of Wonderboard and tile it with some scrap tiles on sale just to get some experience in setting floor tiles? The Wonderboard has two sides, so you can practice tiling twice.