Technically it is not the 4.77 MHz clock what peripherals care about.
Here is a bit of info about the 8284 and the clock generation in IBM PC, XT, and their clones:
The 8284 supports two clock sources, a built-in oscillator, IBM PC and compatibles typically have a 14.31818 MHz quartz crystal connected to it, and an external clock connected to the EFI input. The clock source is selected using F/C pin.
In case of IBM PC/XT, the external clock is not used, and the F/C pin is hardwired to ground, causing the 8284 to use the internally generated clock.
The built-in oscillator produces 14.31818 MHz clock signal on the OSC output, this signal does not depend on the EFI input or the F/C pin value. The OSC signal is buffered and made available on the ISA bus. It is used by CGA, Adlib, SoundBlaster, and so on.
The 8284 divides the clock selected by F/C by 3 for the CPU clock - 4.77 MHz, and then that signal is divided by 2 to obtain the peripheral clock - PCLK, roughly 2.39 MHz. In IBM PC that PCLK is divided further by 2 to obtain a roughly 1.19 MHz clock for the 8253 PIT, which is used for time keeping, sound generation, and memory refresh.
Now, a straight forward, although quite a bit problematic approach to implement the "turbo" mode, is to simply wire a faster clock to EFI, say using 24 MHz crystal oscillator, and use the F/C pin to switch between the standard and the turbo frequency. This approach has several problems:
1. When switched to turbo mode, it will speed up the timer, resulting in time keeping issues, sound being high, etc.
2. The F/C clock switching is not "glitchless", that is, it can result in shorter pulses than either one of the source frequencies, causing all kind of synchronization and stability issues.
3. It will cause issues with the DMA, as the 8237 DMA chip runs on CPU frequency, but it does not work reliably above 5 MHz
4. It might cause issues with extension cards, as they are not designed to run faster... Now ISA is not a synchronous bus, so you can't really say it runs at XX MHz frequency, but rather the timing becomes too fast for certain things, particularly older controllers.
Perhaps some early XT clones used this approach. I personally think only a few did, due to all these issues. But it is quite possible that some people "hacked" their systems this way...
Most turbo XT clones address the issues above as follows:
1. Instead of using PCLK/2 for the PIT, they take OSC and divide it by 12, e.g., this can be done using a 74LS92 counter.
2. Instead of using F/C clock switching method, they implement an external glitchless clock multiplexer, that gets the OSC and the external clocks as inputs, and has the output connected to the EFI input, with F/C tied "high" so that the 8284 uses the EFI input
3. They monitor the DMA requests, and switch the system clock to the "standard" 4.77 MHz clock during DMA requests.
4. They add extra wait cycles in turbo mode (or more naively, regardless of the mode)
Another approach is to use second 8284 to generate the CPU clock only. This addresses the first and somewhat addresses the third issue (DMA always runs on 4.77 MHz, but there are possible synchronization issues) from the list above. It doesn't address the second and the forth issue, unless there are additional circuits to take care of them. This approach is used by somewhat popular PC-SPRINT turbo hack:
https://ctrl-alt-rees.com/2020-03-02-overclocking-the-ibm-5150-8088-cpu-with-pc-sprint.html,
https://github.com/reeshub/pc-sprint)
As long as the floppy works with at least one BIOS, I can call it a victory.