They do. Sata drives and nvme drives both use lba48.
Changes in effective geometry through different translations are very nasty things.
Wherever possible, the use of linear addressed sectors (lba) is vastly superior.
CHS geometry is an anachronism from when drives had stepper motor actuators, and each value had a real representation for where the head array was over the platters.
To help conceptualize things:
These three expressions give the same number of sectors:
16 cyls, 4 heads, 16sec/t (16 * 4 * 16 = 1024 sectors)
4 cyls, 16 heads, 16sec/t (4 * 16 * 16 = 1024 sectors)
MAXLBA=1024 (1024 sectors, linearly)
Suppose your partition table is using the CHS flavor, using the first option.
It says the partition starts at cylinder 15, head 0, sector 0.
Now, suppose you put this drive in another machine, that interprets it using the second option. Cylinder 15 is out of bounds, because the max addressible cylinder is 3. A read error happens.
Now, consider the reverse.
The partition is at cylinder 3, head 0, sector 0.
You move it to the other machine, where it initially acts 'fine'. Reads several sectors fine. Until it tries to read head 5, which is out of bounds. Read error occurs.
With LBA, 'sector 500' is what is asked for. (For example) 'Partition starts at sector 500' is what an LBA style partition table says. OS asks for sector 500, and returns sector 500.
This is the same regardless which computer it's put in.
The different 'kinds' of LBA define the number of bits that are allowed to store the value for number of sectors. 24bit LBA tops out at 16,777,215 sectors. 48bit LBA tops out at 281,474,976,710,655 sectors.
We dont have drives that big yet.