Are/were there any halachic Jewish communities that do/did not have a daily custom of wearing a garment obligated in tzitzith (e.g. tallith katan/tallith gadol)?
Rabbenu Avraham ben HaRambam implies (HaMaspik L'Ovdei Hashem, ed. Wincelberg p. 27) that in his place and time it was not common to wear a four cornered garment with tsitsit.
He is giving examples of behaviours that a person may inappropriately perform just in order to be perceived as pious, and he includes wearing tsitsit constantly. He includes this in the Sages description of yuhara arrogant expressions of excessive religious activity, (Berakhot 17b, Pesahim 55a).
This strongly indicates that wearing a four cornered garment with tsitsit on it was not common there.
Rambam's encouragement that pious people wear tsitsit complements this, (although does not prove it).
שאלני חתני רבי אורי מצוה חמודה כמו ציצית שהיא שקולה כנגד כל המצות מאי שנא דמקילין בה רוב ישראל שאין מתעטפין בכל יום
This indicates that the widespread custom at the time was to not wear tzitzit on a daily basis.