Rigging toggles are simply connectors placed between the stay and the mast tang. They are typically considered an after thought, since they add between 1.5" to 2" of length to the stay. Typically, if a stay comes out a bit short, toggles are used to bridge the gap and connect the stay to the tangs. Because of this, toggles have taken on somewhat of a bad image; broadcasting to the world that the stay was measured a bit too short!
The reality is toggles should be used at the mast tang connection, especially with metal rigging! Metal rigging is very unforgiving when torqued, usually resulting in stress cracks. These cracks in combination with crevice corrosion will lead to the early demise of a steel rigged vessel.
You would think that these wonderful and relatively inexpensive toggles would be in widespread use, but look around and you will rarely see a boat with such toggles.
Toggles add one more axis of rotation to the stay. When the sail fills with wind and the boat heels over, the mast moves! It might move less than an inch, but it will move laterally. In heavy seas, the boat will be pitching back and forth, and the mast will also scoot forwards and backwards with each wave. The combination results in a mast that will move side to side and fore to aft. If your stays are connected to the tang directly, they would only have articulation for fore and aft movements. Lateral movements would cause stress on the fittings which can lead to premature failure.
The addition of the toggle makes the stay a universal joint so the fittings can articulate fore/aft as well as laterally. This will greatly reduce the amount of stress on the terminal fittings which will extend their serviceable life.
Synthetic stays are much less sensitive to these forces, as they are made of rope which can move around more easily. I reused the toggles that were on my mast for the lowers to place the eye splices in a vertical orientation so that their sides would not be in contact. If I had connected them inside the tang, their sides would have been rubbing, leading to chafe and premature failure. At the masthead, the stays are connected directly to the tang because the space was available.
While toggles on metal rigging should be considered mandatory, with synthetic rigging, they are considered a convenience item and used to help orient the eye splices as they connect to their mast end fittings.