They didn't need to see it burn up, that wasn't part of the test criteria.

Gemini 1 was not a test flight of a Gemini capsule, it was a test flight of the Titan II launcher to human rate it. The capsule itself was a dummy, with mostly just a hull and most internal systems replaced by inert components to reproduce the same weight distribution. The capsule itself only had some avionics equipment and sensors to be able to determine how well the launch went.

The disposition of the capsule itself was unimportant for the test beyond the first few hours after launch. It was placed into an incredibly low orbit (with a perigee of just 155 km) and it re-entered after natural orbital decay after only 4 days.

The capsule didn't have the systems installed that would allow it to execute a de-orbit burn, besides which there was a chance that the capsule could be damaged or placed into a bad orbit during the test launch. Holes were drilled into the heat shield to facilitate more complete burn-up during an uncontrolled re-entry, minimizing the risk of some component of the capsule surviving through re-entry and causing damage or injury on the ground.