In the course of working with numerous customers, we have found that a high percentage of them purchase their cable/DSL modems from their carrier. This is not surprising, given the ease of doing it.
I would suggest that there are good reasons to do your own thing. Here are a few of them:
Cost - Some carriers rent modems for a monthly fee, while others sell them outright. Either way, you will likely end up paying more than you would making the purchase yourself.
Security - New vulnerabilities are found daily that expose routers and modems to hacker attack. Although manufacturers are often quick to respond with new firmware to correct the problem, carriers often use a custom version of the products. As such, they can be weeks or even months behind the manufacturer in releasing updates.
Control - When a carrier controls your router/modem, they have the ability to implement functionality that you might not appreciate. For example, when Comcast deploys one of the wireless-capable cable modems, the configure it to offer public wifi service to their customers. This not only can impact your bandwidth, but has the potential to cause future vulnerabilities. They also publish business customers on a public wifi list.
Technology - Carriers have a long purchase, approval, and customization lead time for their devices. As such, they are often behind on technological developments.
As a recent example of why this matters, I was called to assist a customer who had service and a modem provided by a major cable provider. She had consistently experienced issues with her service dropping. After multiple support calls over many months, the carrier finally disclosed that a bug existed in the modem firmware, and offered to do an upgrade. Had this been her own modem, she could have looked for and installed an update much sooner.
In most cases, installing a modem is as simple as plugging it in. While the carriers prefer to sell you their device, they will provide support on customer equipment.
If you are considering making a modem purchase yourself, the carriers usually provide a list of devices they support. Manufacturers often list the supporting carriers right on the product packaging. For your convenience, here are the device support pages for a few major carriers:
AT&T - They are not forthcoming with this information. See DSL Reports for additional information.