Why not? Because we can't.
We don't have full-time communication with Curiosity: Curiosity sends data to the Mars Reconnaisance Orbiter and Mars Odyssey. These are overhead twice a day at 12-hour intervals. MRO and MO are in sun-synchronous orbits, so the planet rotates underneath the orbiter and they cover the entire planet in 1 day.
Both are in orbits slightly under 2 hours long, so they're only above the horizon for a short time.
During those communication passes, a limited amount of data can be uploaded. Curiosity was designed to upload 75 Mbit/day via Odyssey and 250 Mbit/day via MRO. The actual amount varies per day (depending on how high the orbiter is above the horizon), on some passes more data can be sent (up to 500 Mbit/day).
1 image/10 seconds is 6 MB/minute is 360 MB/hour. So you'd saturate the uplink and there'd be no room for science data.
Sending pictures every 10-20 seconds would interrupt driving (you don't want to take images while driving because they'd all be blurry) and hinder science operations. It would also eat into the rover's limited power budget.
The rover drives for a maximum of 3 hours/day. The rest of the time it's stationary so you'd just be sending duplicate images (apart from the occasional mast movement).
The MSL image archive contains all images taken by the rover. Each camera takes images every day. The 2 navigation cameras take 4-150 images per day each, for example. For Sol 2250, about 280 images were taken by the 8 cameras.
Images are usually uploaded within a day, the image archive contains images taken yesterday. Sometimes images are stored on the rover because other data are given priority.
Data for most of this from Emily Lakdawalla's book 'The design and engineering of Curiosity'.