The video can never catch the resolution and bit depth of the still photography. When shooting stills you have plenty of time to collect and process hi-res hi-quality image (huge 3D matrix) while in video you are restricted to 25 frame-per-second rate.
When shooting action stills you have 1 to 10 us for exposure, 200 us for processing and seconds to store the burst of images you have shot. In video you have only 40 us for exposure, processing and storing alltogether. For slo-mo videos you are limitted to 0.3 us capture-process-store period for 3,800 fps video.
Whenever the video reaches a milestone (4K for example), still photography was there years ago.
The restriction of bursts is in buffer size and in data transfer speed.
Just make rough estimate; let's have 18MPx camera with 14bit colour depth and 5 fps burst.
One RAW file is 21-27 MB large.
When shooting 5 frames per second, you have to transfer 105 - 135 MB per second that is 840-1080 Mbps.
For a video you are looking for 24-25 frames per second to have continuous feel. That means 4.0 - 5.4 Gbps data flow.
That's why there is buffer memory that stores the data while slower writing to the memory card is being done. And that's why cheaper cameras can do small bursts while the more expensive ones can do longer bursts - they have much larger buffer.
If you add some compression algorithm in the line, you have to add the processing time (another limit for the frame rate) but you can reduce the data rate depending on the compression algorithm used.
Note on data transfer:
The most common way to connect DSLR to PC is USB 2.0 with maximum speed of 480 mbps (not even close). USB 3.1 gen.1 can transfer data with speeds up to 5Gbps (close). USB 3.1 gen.2 and USB-C are planned to reach speeds up to 10 Gbps.
You have to write all the data down; commonly used SD cards are capable of various transfer speeds:
SD UHS 1 class guarantees 10MBps = 80Mbps write speed;
SD UHS 3 class guarantees 30MBps = 240Mbps.
SD V90 class guarantees 90MBps = 720Mbps.
Fastest CompactFlash card can reach 160MBps with 65MBps guaranteed (1280/520 Mbps).
The fastest XQD 2.0 cards can reach 400MBps (3.2 Gbps).
The fastest CFast 2.0 cards can reach 490MBps (4.0 Gbps).
Hard drives connected via obsolete PATA interface can reach 536Mbps speeds,
Hard drives conencted via SATA 3Gbps or SATA 6Gbps can theoretically reach 3 or 6, respectively, Gbps. SSD drives are advertised with speeds up to 680 or 1040 Mbps writing speeds. Old hard drives use buffers, I cannot tell what are their speeds when the buffer runs out (the largest buffer I can find is 256MB; the room for 10 RAW frames!).
You can see that no storage is capable of writing such ammounts of data steadily for long periods and only the high spec USB 3.2 and USB-C can handle such data rate.
Only the 256 GB Delkin card is capable to be fairly close to the desired speed. Its memory runs out in 7 minutes and 45 seconds of video.