Why specifically use Passata, rather than tomatoes, in Ragu?

The primary reason is definitely convenience. If you don't want skin and seeds in your sauce, then you have to do some work to avoid it. Yes, it's possible, e.g. passing through a food mill, or blanching and peeling plus retaining only the flesh, but having it already done is a whole lot easier.

Passata is usually much thicker too, so it won't need as long a cooking time to reduce into a non-watery sauce as fresh tomatoes. On top of that, you don't have to worry about whether you can find good fresh tomatoes, e.g. if it's winter and they're out of season.

Your two cases for comparison seem to overlook this: if you just chop and cook, you'll have skin and seeds in your sauce, as well as excess liquid to cook down, while if you use passata, you won't. (Also, for what it's worth, you'd need pretty giant tomatoes to get the equivalent of 3/4 cup of passata out of one tomato.)

Of course, if you don't mind skin and seeds, it's also perfectly fine to simply cook fresh tomatoes and be done with it.

Note that you can often get similar advantages from other canned tomato products. In the US, crushed tomatoes are far more common, and a roughly similar texture. (Peeled whole tomatoes, diced tomatoes, tomato sauce, and tomato paste can also be useful depending on what texture you're aiming for.)

There are many advantages to using passata for tomato sauces:

• no seeds, no peels (canned tomatoes often are the same in this respect)
• general lower water content as tomatoes are drained before being shredded, which means you don't have to wait for that water to boil away in making the sauce thicker
• very easy to preserve, as if it's not opened it can be kept around for years unrefrigerated.

However, in the context of ragù, you should not use passata but concentrated tomato paste instead. Ragú is a long preparation in which you are removing water all the time:

• from the meat, to correctly sear it at higher than 100°C temperatures
• from the vegetables, when sauteeing them to make soffritto
• from the other ingredients added for fat content and flavor afterwards, such as milk or cream, and of course tomatoes.

After the initial searing, it is true the long cooking time of ragù needs a wet environment to break down collagen and make the meat tender. However, you don't want to prolong this time even more by having additional water evaporate. So you can save yourself some time over the standard 4 hours and use tomato concentrate.