The map on osm.org is not really meant for use as a map; it is more of a feedback tool for mappers to see how their changes render.

Instead, use a dedicated app like CoMaps or Osmand or websites like osmapp.org or cartes.app.

The feature you are describing (handling each object seperately) requires a lot more processing power on both the server's and user's part than just displaying a map image like osm.org does. This is why the OSMF have decided to use their limited resources on supporting the openstreetmap database, while leaving the map- and appmaking to others. This is also why websites that try to emulate a google maps-like experience like osmapp and cartes feel pretty slow when using them.