It's pretty simple really, the reasons I would want an inverted (pull behind) blower are:
You can look and drive forward when snow blowing, no neck aches at the end
You can leave the loader on for things like moving firewood
If you want a compact package with high maneuverability you can remove the FEL, this is also an advantage of a typical rear blower over front mount
The rear blower in the back makes a great counter weight
When your done snow blowing you have no tracks behind you, it looks so nice and neat, this doesn't really matter functionally of course
If you use your tractor for just about anything else in the winter you don't have to remove your front mount snowblower, like when logging for firewood through the woods
You can back right up close to garage doors and scrape the snow away, using it like a box blade in a sense
You have excellent visibility of what is going into the snowblower
These are just a few examples off the top of my head. If you want to see one in action then YouTube "inverted snowblower tractor" or something to that effect.
There is a good reason why inverted snowblowers are the "go to" style for people who do snow removal as a business. When you really think about it, it actually makes the most sense in the majority of cases, but of course there are exceptions. A lot of people can't seem to get over the fact that you have to drive through the snow before blowing it, which really isn't that big of a deal when your properly ballasted although some people would need chains as well.
I don't think an inverted snowblower is a good choice on a very low clearance tractor lightweight tractor or when the operator lives somewhere that routinely gets 2' or more of snow on a regular basis, which is not all that common.
I think another great option is the FEL mounted hydraulic blower like Grsthegreat has. For his situation that can't be beat, but for most, I still think an inverted blower would be a better choice.
To be honest, I can't fathom why anyone wouldn't want a pull behind snowblower.