This is an unfortunate attitude which seems to bubble up every time someone asks a question on asynchronous design in, e.g., the Xilinx forums. Just because "proper RTL design" was drilled into everybody's skull in school, and for good reasons, does not mean there aren't legitimate reasons to deviate from it. TDCs and HRPWM come to mind.
You can use a microscope to drive down nails too, but it doesn't mean that's a good idea, or that many people will sympathize with your complaints about how inconvenient microscopes are for driving nails. FPGA is a tool designed for synchronous applications. You pick a tool for the job, and not the other way around.
And yet numerous published papers on, e.g., FPGA TDCs exist, and they are used in production (CERN and elsewhere). You may dismiss these as niche applications but it seems to me unnecessarily harsh to offer blanket discouragement of this sort of thing. Wouldn't you agree the tools should have an "I know what I'm doing" mode, which is not too obscure or difficult to find? I am not objecting to reasonable guardrails, but it should be possible to circumvent them easily, and inquiries along these lines should not be seen as somehow wrong-headed, unless you know what the person is attempting to achieve.
Saying "CERN uses this in production" is like the small software vendor saying "IBM uses our application!" Sure, maybe one person at IBM thought the software was useful for a particular task (and there's no reason to doubt this), but that doesn't mean that the whole of IBM uses it or even knows it exists.
As for "unfortunate attitude which seems to bubble up every time someone asks a question on asynchronous design in, e.g., the Xilinx forums," be honest -- most of people asking on the Xilinx forum about async design are newbies who need those guardrails.
And here's the thing: most professional FPGA engineers deviate from fully-synchronous designs all the time. We do it every time we need to cross a clock domain, or handle an asynchronous bus from an external device.
I looked and
found a CERN paper on TDCs and it is interesting. The Vernier delay line (figure 6) is a clever way of abusing the fabric. I wonder if you could even do this is in a new FPGA where only global nets route to the flops' clock inputs. But, let's be honest here, this is a 64-tap delay line to achieve a specific goal, and not a general-purpose design technique!