Default entity ID for _entity_view in routing.yml
The default ID can be set in the defaults section, here is an example:

my_module.view_dashboard:
  path: '/admin/dashboard/{my_entity_id}'
  defaults:
    _entity_view: 'my_custom_entity.full'
    my_entity_id: 123
  requirements:
    _role: 'authenticated'
    my_entity_id: ^[0-9]+
  options:
    _admin_route: true
    parameters:
      my_entity_id:
        type: 'entity:my_custom_entity'

my_module.view_stats:
  path: '/admin/stats/{my_entity_id}'
  defaults:
    _entity_view: 'my_custom_entity.full'
    my_entity_id: 456
  requirements:
    _role: 'authenticated'
    my_entity_id: ^[0-9]+
  options:
    _admin_route: true
    parameters:
      my_entity_id:
        type: 'entity:my_custom_entity'


This solution creates nice URLs without any controller.