You are correct, but it's not gamebreaking
You have listed the only circumstances the DMG provides with regard to when the Roc-like creature will disappear, but also note Magic Items: Quaal's Feather Tokens limitations (DMG, "Magic Items", Quaal's Feather Token: Bird) :
The bird has the statistics of a Roc (MM, Roc), but it obeys your simple commands and can't attack.
What you've got is a gargantuan creature that can carry stuff, fly quickly, and has pretty good perception. It can't attack and is therefore more of a support creature than something that's going to be useful in combat or other circumstances.
Untrained mount with a large carry capacity
Whether or not it can carry an entire party and their belongings is also up for discussion. Mounts don't discuss multiple riders and a concern about fast party travel speed is definitely limited by who can 'ride' the Roc. Having a transport that can only have a single rider (and remember, this is an untrained mount) and is capable of carrying a lot of objects really gamebreaking?
Probably not, and even if you've got a 'puzzle' where your players have to figure out how to return a heavy object to another location, this is a great solution for a one-time use Rare magic item.
But that fly speed (and other considerations)
Yes, 120 is a very fast speed, but that's a fairly easy thing to mitigate if there is combat or threats in the air. Alternatively, not always having the airspace for your PCs to play in is another obvious option. Hard to bring a Gargantuan creature inside :)
Simple Commands Only
The Roc only has an INT 3, which implies it is not an intelligent creature that can act independently and can only
obeys your simple commands.
What happens when it experiences an event that requires it to react is going to come down to table play and how wide of a berth a DM gives those simple commands only to their player.
Theik's answer brings up a very interesting discussion. What is meant by >disappears after flying its maximum distance for a day
Does that mean:
1. Disappears after flying its maximum distance for a day (144 miles)
2. Disappears after flying its maximum distance for a day (144 miles in a day)
#1 is what Theik is proposing, but #2 is an equally valid interpretation.
However, as Tiggerous commented, why include the "day" language if the limitation is simply 144 miles? BY including it, it suggests that #2 is the correct interpretation.
Each token gives a different duration rule, so we can't completely use them as references, but they do give some guidance:
For the next 24 hours
...for 8 hours. You can dismiss the fan as an action.
The boat remains for 24 hours and then disappears.
The whip disappears after 1 hour, when you use an action to dismiss it, or when you are incapacitated or die.
Each of these, except for the Tree, have a specific time duration. The Bird and the Tree do not have a time duration. Whether or not the Bird's duration is limited by total distance used ever or by total distance used for a day is a matter of interpretation that has not been clarified by the designers and is therefore up to the DM to determine at their table.
Ruling that the Bird Token is limited to just 144 miles of travel is a legitimate rule, but consider why you need to rule that. Is it an absolutely necessary ruling for 'balance', or is the Bird Token's already nerfed Roc okay for daily use until it drops to 0 HP?
Hungry hungry hippo
While this bird was created by magic, it's a bird with the stats of a Roc. And a Roc's gotta eat, just like Find Steed. And they mostly eat a LOT of food
A roc seldom hunts swift or small creatures, and it ignores towns and forests where prey can easily take cover. When it locates a large and slow-moving target such as a giant, a whale, or an elephant, a roc dives down to snatch its prey in its massive talons.
A longer life of the bird is definitely balanced by the cost of feeding it.