I guess you are talking about Turbo XT machines running software written for original XT machines. This 4.77MHz speed was assumed in software written for the original IBM PC. Turbo XT's turbo button brought back the speed from 12MHz or 8MHz back to 4.77MHz for full compatibility.

The turbo button on later machines couldn't bring down the speed to 4.77MHz, thus you lost compatibility with original IBM PC speed no matter whether you run full speed or crippled speed. But by that time, software generally stopped assuming any certain clock speed, and speed-sensitive bugs would be indeed bugs rather than a side-effect of targetting a specific platform in the software.

Some software I remember hated anything faster than 4.77MHz was Copy II PC. It just fails to read or write disks if you run it on anything faster than 8MHz IIRC, especially its earlier versions.

VGACopy was another software that crashes randomly on startup if you run it on a very fast machine.

Fantavision's animation speed goes way out of the roof on fast machines. Same for Banner Mania.

I'm pretty sure some more serious productivitiy software required the slow speed too, but I can't confirm. Probably dBase.

I find a lot of older demoscene software is speed sensitive.

Scream Tracker 3 I ran into an issue where it wouldn't detect on the mixing speed properly on fast machines (e.g. P4).

The above mentioned animation software are also examples.

Interesting topic. I asked my dad, he can't recall any scenario right now. 🤷‍♂️

If you ask me, I'd say floppy access and communication programs.
Timing-sensitive things like speech synthesis, too.

Some games like The Last Half of Darkness had different speed settings, too.
Games that were "real-time", ie not turn-based, could need the brake, too.

Edit:

wbahnassi wrote on 2024-02-24, 19:48:

The turbo button on later machines couldn't bring down the speed to 4.77MHz, thus you lost compatibility with original IBM PC speed no matter whether you run full speed or crippled speed.

That's not a bug, it's a feature. 😁
- No, really.

I do have an 4,77 MHz XT class PC and it's incredible slow.
It feels barely faster than PC-Ditto emulating a PC on an Atari ST.

In retrospect, I'm so glad my dad did give an used 12MHz 286 PC w/ VGA to me.

It was very dated by the 90s, but it was upgraded (handy scanner, 2x CD-ROM, soundcard) and did at least don't hurt my nerves.

I'm not sure if I could have had mentally handled an 8088 PC back in the 80s.
Or a Sanyo MBC-550.

I mean, an XT w/ 8088 is technologically fascinating.
To see Windows 2 or GEM actually running on that calculator chip is amazing.
https://www.youtube.com/watch?v=gCV8OPVY-uE

Watching it crawl, I mean. I have programs written in QuickBasic that plot data read from gameport (say, temperature sensor).
On an XT, the curve draws in slow motion. Almost artistically.

I also have some radio programs like Hellschreiber that run cozily on an XT.
https://www.youtube.com/watch?v=l2zLL0Z-zI4

A few CAD and astronomy programs, too.
AutoSketch 2 or 3, Expert Astronomer etc.

Or that MCS BASIC-52 emulator..
https://www.youtube.com/watch?v=vehMmCONQWo

However, if I had been asked to use an XT class PC on a daily basis - oh well! 😰
I'm not sure how long I could have stand this.
I'd probably replaced the XT motherboard ASAP, keeping the rest of the PC.

Because, Hercules and the slow HDD wasn't that bad.
Windows 2 and 3 worked acceptable with it.
With lots of dithering going on, sure, but a 286 or 386SX would handle this.

A little RAM disk drive could have had make up for the slow HDD, too.

Update. There's another use for the Turbo Button (or Turbo Brake) that comes to my mind: Experiments with the gameport.
On a slow PC, the range of measurement is greater - because the capacitors have more time to charge.
That's important if we're tinkering with sensors, like NTCs or photodiodes.
So a 4,77 MHz PC with a slow 8088 CPU makes for a nice lab PC here.

So with a fast PC, we have two options to fight this issue
a) to slow down the PC (slowdown utility, turbo button)
b) to add bigger capacitors to the game card

Option b) might be difficult to do, because many ISA soundcards of the 90s have an integrated gameport circuit.

The unlisted option c) would be to use gameports with speed-compensation, maybe.
I say "maybe", because I don't know how they exactly work. 🙁
Most importantly, they must be able report the maxium values of a joystick (full range).

Flashing cursors in DOS and DOS-based word editors might be disorientating if the CPU is faster than BIOS/DOS thinks it is, too.

It started, as correctly mentioned by wbahnassi, as a means to ensure compatibility with the original IBM PC.

It then continued to exist as a possible solution to any issue because of speed. A well known non-gaming example is the Runtime Error 200 - divide by zero of Turbo Pascal applications that use the crt unit.

Agreed. But the original IBM/AT Model 5170 sort of was a reference, too. Not just the IBM Model 5150 (and near identical 5160).
So it makes sense that AT class PCs w/ Turbo Button tried to match original PC/AT speed (or speeds; 6 and 8 MHz), rather than PC/XT speed.