Bonus resources are not removed when founding cities (they are removed when building districts and wonders), and (as pwoz notes) some YT streamers have settled cities on known luxuries, bonus resources and (IIRC) strategics. Whether settling on a bonus resource makes sense depends on the base yield of the tile before the city is settled. If the tile (with the bonus resource) provides no more than 2 food and 1 hammer, settling on the bonus resource tile confers no benefit (since founding the city just increases the city center tile yield to the minimum of 2 food and 1 hammer, if the base yield is less than 2 food and 1 hammer). If, however, a bonus resource tile has a base yield that is higher than 2 food or 1 hammer, that excess yield is preserved. So, for example, settling a city on a flat grassland cattle tile (base yield 3 food) will result in a city center tile yield of 3 food and 1 hammer (and the extra food benefits you all game long, in contrast to the short-term boost you would get if you settled on another tile and harvested the cattle instead).
As an aside, that is why settling on a plains hill is so beneficial -- because a plains hill has a base tile yield of 1 food and 2 hammers, settling on a plains hill will result in a city center tile yield of 2 food and 2 hammers. In contrast, settling on a grassland hill (where the base yield is already 2 food/1 hammer) or a desert hill (where the base yield is just 1 hammer) results in a city center tile yield of 2 food/1 hammer.