Streaming services are not created equally.  They use different formats and the stream itself is adjusted on the fly to try to deliver the highest resolution content to you without buffering.  

What is a more accurate story?  Here is a rough "data burn rate guide" you can expect for codec and screen resolution.  Better, faster connection allows you to pull more data.  The stream can also be broken up into as many as 12 streams at different resolutions to try to find the highest resolution one it can deliver, so this is going to vary a bit, and it isn't the entire story either, but it is closer to the truth.    

The codec the streaming service uses comes into play too, so when they say "hours of streaming", it's not the whole story.  Netflix uses H264 for example.  Some streams you find are H265.  This is a rough guide of the bandwidth you would use to avoid buffering.

                                  H264        H265
1280×720(HD)        3Mbps    1.5Mbps
1920X1080(FHD)    6Mbps    3Mbps
3840×2160 (UHD)  25Mbps 12Mbps
4096×2160 (4K)     32Mbps 15Mbps

In terms of GB/hour:

1280×720(HD)        1.35     .68
1920X1080(FHD)     2.7       1.35
3840×2160 (UHD)   11.25   5.4
4096×2160 (4K)       14.4     6.75

If you have a 1.2 terabyte data cap per month, that's 40GB per day.  Maybe you don't use the internet every day.  Maybe you use it all the time.  40GB/day is just a reference.  Typically burn more than that every day?  You'll be over the cap.

Perhaps you can set the max resolution on your streaming device to something under 4K to save data.  It could be the app settings on your streaming device really don't work that great.  I've seen that with Roku and Hulu despite what I set on a TV.  Some say Peacock's network is a data pig.  Other apps  don't have video quality settings.  I throttle devices with a firewall to avoid the data cap, then the settings on streaming devices do not matter.