Alternative to backer rod and bond breaker tape for caulking

A 5/8 inch gap is an awfully wide one to try to bridge with silicone caulk. Even with some type of filler I think you are unlikely to get a result that you would be happy with. At least I know I would not be happy.

Silicone caulk needs to be applied all at once to get a nice installation. First off it will not be reasonably possible to squirt out a 5/8 inch bead from a typical caulking tube spigot. Next consider that silicone material applied as a secondary application will not bond and adhere to previously applied bead that has cured.

If I had your issue I would be investigating filling up a majority of the gap area with a tile setting cement that is compatible with the backer materials behind your existing tile installation. I would then cut narrow pieces of tile (you could even band with a contrasting color) that you would set into additional tile setting cement such that it was flush with the existing tile surface. Once these strips were in place grout the spaces between the tiles and strips. Finally finish off with a neat narrow bead of the silicone material in the corner around the tub surface.

There isn't anything wrong with grouting between tub and tile given that you do it right. I fill up tub full of water (weight) and grout. I feel grout is just easier to deal with. My grout has lasted 6-7 years now in one bathroom without any sort of cracking or separation. If there was separation I would caulk it.

It does get mildew and mold and I probably spray it with cleaner once every 4-5 months. That is about it.

From what I can tell from your pictures, that doesn't seem like grout. And if it was grouted it was done very poorly. That looks like a mastic or even a white thinset to me. And then caulked over. It also looks like too big of an area to caulk. I would suggest trying to break out some of that area and then going over it with grout. (Also it looks like crappy caulk. I would use silicone here)