Basically any computers from the mid 90s and earlier perform a slow memory check on every single boot. The more memory there is present, the slower that process becomes, for example: https://www.youtube.com/watch?v=A3Po8zneaLE
Why are they doing that? Modern computers, as far as I am aware of, only check their memory when explicitly told to. What exactly are retro computers doing during that check that more modern computers seem to not do and why?
Why are they doing that?
The most important reason is that IBM introduced that check as part of the BIOS startup code, so everyone copied it to be compatible.
The PC did differ from many other machines of the same era in that it did a thorough test of all components installed at power up to make sure the configuration was operable. Something carried over from mainframes or similar professional systems. Other machines just initialized components and let the user guess what the problem was when an error occurred.
Modern computers, as far as I am aware of, only check their memory when explicitly told to.
RAM got more reliable over the years. Equally important, RAM size increased manyfold, making a thorough memory test anything but quick. Last but not least, memory design for PCs did split in the (late) 90s between consumer PC with error detection (like the first PC) and professional machines with error correction (ECC). Where consumer grade machines just let the process/OS die on the user, professional systems will not only correct starting RAM failure, but also report it which (hopefully) leads to preemptive RAM change.
What exactly are retro computers doing during that check that more modern computers seem to not do
Various bit patterns are written to RAM and read again to detect cell failure or certain kinds of crossover. The test is split into two parts: base RAM (first 16/64 KiB, *1,2) and memory above 64 KiB. On AT (286+) class machines, a third (faster) test may be used for memory above 1 MiB (*3), together with an additional test in protected mode and even more diverging POST codes.
Conventional memory (up to 1 MiB ,*4) is checked in 4 KiB blocks (*5) and reported as such. The BIOS halts if there is an error in the first 16 KiB (original PC) or first 64 KiB (XT and above).
The bit pattern used (*6) for the first 64 KiB is AA, 55, 00, FF, 01, 02, 04, 08, 10, 20, 40 and 80. They are written (and read) in a way to not only detect single bit failures, but also address and data line mismatch/failure.
For the remaining memory it is shortened to AA, 55, FF, 00 and 01.
Here is a nice explanation of basic bit walking and increment tests similar to what the PC does/did and what it will show.
and why?
To alarm the user of an imminent RAM problem before it occurs so that they don't lose hours of work due to a flipped bit.
*1 - 16 KiB on the first series of 5150 PCs (64 Kib Motherboard), 64KiB on the later (256 KiB motherboard and XT)
*2 - On the XT there is a separate BIOS POST code for the first 32 KiB.
*3 - The beep codes do not distinguish between above 64 KiB and above 1 MiB.
*4 - Well, in reality on the early PCs only until 544 KiB. Later PCs would go until 640 KiB.
*5 - Looks like a hint as if they expected 4 KiB chips to be used - at least during early development stage - or that test was copied from some other device using them.
*6 - Caveat: Bit patterns are taken from an old man's memory. To verify, browsing the BIOS would be helpful.
In the era of the original IBM PC (early 1980s), home computers would often use many chips of RAM (eight or more) to provide the system's memory. These would either be soldered directly to the motherboard, or fitted in individual sockets. (The inline memory modules or SIMMs/DIMMs we see today, with several RAM chips soldered to a removable board, came years later.)
Memory chips can fail in a variety of different ways. For example, they might always output some fixed value, fail to retain or refresh stored data, write or read data to/from the wrong location, or something else entirely. Some errors will stop the operating system from booting correctly, others may only show up later when running your software (and potentially corrupting your important data!)
To avoid this happening, the IBM PC's BIOS runs a series of read and write tests on its memory during the Power ON Self-Test (POST), before handing over to the operating system. If an error is detected, a message is displayed on-screen which a technician can use to determine the faulty chip. (In a fully expanded IBM PC, there'd be 36 AM9016 memory chips; finding a faulty chip by trial-and-error would be time consuming.)
As mentioned in the question, the more RAM fitted to a machine, the longer it takes to test all memory locations in that RAM. Because nobody enjoys waiting for their computer to boot, the option to skip the extended memory test was included. Improved manufacturing techniques meant fewer RAM chip errors, and it was often the case that a detected RAM fault was caused by a RAM chip that had become loose in its socket, a phenomenon known as "chip creep". Frustration with this situation led to the introduction of SIMMs, which were held in position more reliably, and also saved space on the motherboard.
Because memory tests were becoming slower, and faults were becoming rarer, manufacturers changed the default to not running a memory test during POST. (A faster boot-time would be a marketing advantage.) The BIOS option is still available on modern machines, usually by disabling an option named "fast boot" or similar.
The PC's POST tests routines are an inheritance from the Datamaster's PID 1200 routine (see it here in action), which is an exhaustive test of all the system and allows detection and test of ROMs, RAM and peripherals.
When IBM designed the System/23 they used the same methodology as a they would as if it was a minicomputer (midrange system). On every single boot, the Datamaster would test itself to be easier to diagnose and repair.
Later on, when it was modified to be the first PC prototype, they wrote their equivalent of the PID 1200 which is the original POST system.
