I can't speak to TAMU's ID program.
I have a degree that is in the ID field (Logistics and Supply Chain Management) from a school in the Pacific NW. The study is basically that of business operations -- how to make a business operate effectively, efficiently, and set and meet goals.
Starting out post college is difficult for most of the people I graduated with. Historically, the people that work in operations fields have started out on the shop floor and worked their way up, and people with degrees but no experience don't get a kind reception. This was starting to change, but slowly when I graduated ten years ago. It will continue to change as the older workforce retires.
Back on the other hand, it gives you the mental toolset to figure out just about any business system that involves moving things from A to B. It gives you the tools to analyze the before and the after and explain it in both engineering terms and financial terms. Personally, I work in IT. I use the capacity planning knowledge from the textbook I used in school ten years ago to plan capacity for certain IT systems. The math is all the same, and the nature of using formal logic in business environments is the same. Often, you end up having to straddle all of the different "silos" that businesses form internally. You get goals from finance people, you get timeline and needs from marketing and customer service, and you get constraints from the actual shop floor (or implementation teams.) One aspect of the job that an ID/SCM person does, at a higher level, involves going between the different departments and making sure that they understand everyone else. It's a useful skill to have and a useful role to have been in regardless of industry.
My sister graduated from the same program I did and now works as a buyer for Williams Sonoma. She decided that she wanted to work in fashion buying, and worked her butt off for five years before she got real traction. Ten years after graduation, we are both in relatively demanding jobs, but we're also making very decent money for anyone in any program. For several years, we both made more than my fiancée, who is a full on engineer with a master's and a PE, although that may be due to cost of living.
Industry-wise, here in Texas I could see myself quitting IT in a few years and going into O&G or managing building projects. Things that people with SCM or ID degrees are suited for include, as previously stated, operations management, purchasing and buying, shipping and transportation, handling the legalities of shipping and the UCC (more important and fussier than you think...), project management on both large scale (capital improvement projects) and small (shop floor jobs), PRODUCT management (which is what sometimes the go-between-silos role I mentioned is called but this is usually handled by people with more marketing experience), and related roles that nominally fall under IT and Sales. Sound broad? It is. That's part of the problem that people have starting out.
TAMU's ID program, from what I heard, is better than the one I went through because it's got a larger engineering component. There's more math and formal logic. Besides the "how to talk to people in other specialties" classes, math was actually the most useful part of the degree I got. The second most useful part, and what actually pushed me towards IT, was an elective that involved implementing and programming a small ERP package developed in MS Access. (Development = Coding the raw software, which we didn't do. Implementing = customizing it for our needs. Programming = Putting in our Bill of Materials and making it do interesting work. Obviously not something I'd use in a real job, but it was incredibly illuminating to see how complicated these things are and how fast a single bad entry can make a mess.)
If you think you might be excited about this field, go read
The Goal. If that sort of problem solving sounds exciting to you, then you should pursue ID. If it seems like a pain in the ass and that you're reading someone else's religious moment but not actually catching the holy spirit yourself, then go find a different field to study. It's worth it to buy a copy; I would give you about a 75% chance that you'll end up having to read it for a class.
