What would constitute a need for a high bit rate capture?

The answer to pretty much all your questions is one word: video. Exact details of bit rates, video formats and whatever else are off-topic on this site which is about still photography so I won't go into it here, but basically you don't need to worry about this unless you intend to shoot video.

One thing to note though: the speeds quoted for SD cards are read speeds. Cameras don't really care about read speeds, but they do very much care about write speeds - it's perfectly possible to get cards which have a high read speed but a mediocre write speed, so always be careful when buying a card.

Log sampling and 4K video, are two different things. The first one is about how the video data is recorded, $k is simply put the resolution - or how many pixels of data you record.

As for the original question real world scenario that meets the high frame per second shooting of still images for longer (that's the only time when the write speed of your sd card matters), think of shooting a whirling oriental dancer at a performance (that's what I do), trying to carch them mid-turn, facing the camera, and going for the perfect facial expression. More generically, dynamic sports where action takes longer than an instant (think wrestling rather then boxing), or wildlife (a hummingbird circling several flowers, rathen than a soaring eagle).

The write speed of a SD card is specified as its "class", which is the important characteristic when using the card for video.

Most of your concerns are exclusively about video capture. The higher the resolution (how many pixels wide and tall your video has), the higher the frame rate (how many frames per second your video uses), and the lower the compression (how many slightly different colors are grouped in the same bucket as a single color - that's a bit simplistic but conceptually accurate) - then the more data per second you need to save to your memory card.

For still imaging, the only real concern is if you are planning to shoot a large number of images in long, continuous bursts. This is something those who shoot action and sports are concerned with. Shooting still images of performance art is another area where sustainable burst rate is important.

Assuming the card is the limiting factor, the faster your card can write data, the more frames you can take in a burst before the camera begins to bog down as it waits for data to be written to the card so that more room can be made in the camera's internal memory buffer to store the next shot. Once the camera bogs down, the faster your card can write then the faster each succeeding frame can be taken.

For example, I have Canon EOS 5D Mark IV and 7D Mark II cameras. Both of them have a Compact Flash slot and an SD card slot. The CF card slot runs at a faster bus speed than the SD card slot does.

• With the fastest CF cards, the camera can write a little over 100 MB/s (Megabytes per second. Since one byte is made up of eight bits, one MB/s is equal to eight mb/s or megabits-per-second). For the 7D Mark II that means I can shoot around 120 raw images in a 30 second span. For the first three or four seconds the camera fires at the maximum burst rate of 10 frames per second. After that it slows down as each additional frame can only be taken when enough memory in the buffer is made available after an earlier image has been written to the card.
• With the fastest SD cards, the cameras can only write about 75-80 MB/s. This is because the bus speed of the card slot is only UHS-I compliant. There are much faster SD cards available that use UHS-II, but the bottleneck in this case is the speed of the connection between the camera and the memory card in the SD slot. For the 7D Mark II that means I can only shoot about 95 frames in a 30 second span. The camera still fires at the same 10 fps for the initial 3-4 second burst, but then it takes longer between each additional frame as it takes longer to write each image to the memory card.

If I use a slower card in either slot, the burst rate is even more limited. An old CF card I've had for well over a decade can only write at about 15 MB/s. Once it bogs down, it takes well over one second to write each photo to the card! In a 30 second burst, I can only get about 40 images captured. The first thirty frames are still captured in the initial three second burst, but then only ten more additional frames can be taken in the following 27 seconds!

From speeds you mention, it seems like you were looking at Lexar SD cards. The speed prominently displayed at the front is read speed, while write speed can be dramatically lower.

250 MB/s read, but only 120 MB/s write speed

300 MB/s read, and 260 MB/s write

Much more significant difference in writing than reading speeds as well as a different class of sustained write performance. That makes the price difference much less surprising.

Speaking for the X-T4 specifically:

It can record video at a maximum bitrate of 400Mb/s (Mega Bit) which equal 50MB/s (Mega Byte). Have a look at the video rating (V30, V60, V90) of the SD Cards you are considering. The number after the V tells you how fast it will write continuously, it's the guaranteed minimum writing speed in MB.

So if you want to go with the highest quality bitrate of 400Mb/s than you need at least a card with V60 on it.

For shooting photos in burst mode (i.e. 15 images per second) in RAW + JPEG (= roughly 65MB per image) you would need writing speeds of nearly 1 GB/s. As no current SD Card can handle these writing speeds, the camera writes those images to its internal memory first and then starts to slowly store them on the SD Card. If your card is fast, the camera is able to maintain the high speed burst mode for longer until it needs to slow down as its internal memory starts to fill up. Only then you will benefit from the faster cards.

To conclude: The problem here surprisingly is not the video part but rather the photo part. Just keep in mind that shooting video in 400Mb/s will give you roughly 42 minutes of recording time until a 128GB card is running out of space.

NB: On the X-T4 you can choose the SD Card slot where photos and video go to separately. So for the best price/performance ratio you can go for a cheaper V60 video card and a more expensive card for photo.