I have used plastic water bottles with pretty good success. They are light weight and take up the unwanted room in your pot.

Dramatic changes in texture cause water passing through the soil to back up until the soil becomes saturated before the water then rushes out - there is a possibility of the bottom half of the soil being too wet much of the time. This is why when you buy drainage sensitive kinds like rhododendrons and knock them out of the pots later the lower part of the soil may fall off, them never having rooted down into it. So if you fill half the pot with bottles the plants may end up living mostly or entirely in the top 1/4 of the pot only, depending on how they react to the moisture situation that may be created by the pot being half full of material that is very much coarser in texture than the soil.

I have successfully used packing peanuts.

Your plants survived the packing peanuts. By the time you pay for the pots, plants, fertilizer and soil why be concerned about the additional cost of filling the whole pot with soil?

Of course, in a big planter on a roof there can be a need to reduce weight.

I had the same question and I would think that the size of the pot and what you grow in it would make some difference in adding filler in part of the pot.

There's always a perched water table where the water traveling down through the pot hits a change in consistency. With soil all the way to the bottom of the pot it is the bottom of the pot that causes the water to hesitate and saturate the soil before exiting. When drainage material or filler is added then that layer of recurring sogginess is pushed up higher in the pot, reducing the amount of usable soil. If a pot is already a low and broad shape the layer of adequately aerated soil can become very shallow.

I've never used a filler in a pot. Never saw the need for it, but I'm not growing anything in pots on the roof.

I grow many things in containers of all sizes, including many permanent type plantings (Japanese maples, conifers, various shrubs) and I agree using fillers (rocks, packing peanuts, empty water bottles, crushed pop cans, etc.) is not a desirable practice for the reasons outlined above.

The cache pot method does work well or you can purchase specially designed pot inserts that effectively lift the soil level in a deep pot to avoid the perching yet reduce the soil needed/lighten the filled pot.

A pot in a pot also keeps the media cooler when the son shines on it.
Mike