It's not leaking that's the concern. It's that not having the names of objects be easily enumerable is a strongly security-enhancing feature of a system.
Yes of course everyone should check and unit test that every object is owned by the user or account loading it, but demanding more sophistication from an attacker than taking "/my_things/23" and loading "/my_things/24" is a big win.
With a single sequence and a busy system, the ids for most high-level tables/collection are extremely sparse. This doesn't mean they can't be enumerated, but you will probably notice if you suddenly start getting hammered with 404s or 410s or whatever your system generates on "not found".
Also, if most of your endpoints require auth, this is not typically a problem.
It really depends on your application. But yes, that's something to be aware of. If you need some ids to be unguessable, make sure they are not predictable :-)