On an anglo, thumb straps would inhibit the use of the air-button and left-hand drone button (where fitted).

You regard "static work by the thumb" as a disadvantage. If find it is helpful to keep the straps slack enough to let my hand move sufficiently to reach different fingering positions. The thumb can be then be used to tension the strap when required. If my hand were more firmly fixed in place it would restrict my playing.

One of the contributors to the c.net discussion says he is not 100% happy with the shaped rests on his instrument for this very reason.