I caught some words from a retired now Engineer him worked at Fluke.
He admitted that fast continuity mode this is made by adding one separate hi-speed comparator (It doesn't depend on a conversion).
This is a story relative to Fluke 8060 Handheld multimeter.
Speaking of DMM development techniques of the past, this above example could be seen as smart engineering this simile to simple practical solution which did the trick in 90s.
It does not required much of imagination so we in 2017 to understand that any modern engineering relative to a multi factional continuity mode, this will never be that fast in a race with a single hi-speed comparator.
For example newer multimeter with smart continuity mode ( this performing a measurement and continuity sound gets out when low threshold value detected) or other functionality as for example LCD back-light gets on and off, all such added features they will steal away a few milliseconds response time from the beeper.
Therefore it is reasonable, all of us to re-evaluate our expectations.
Here is a good example this coming from the world of Oscilloscopes, Analog oscilloscope tube screen response theoretically this could be as fast as the speed of light.
Modern DSO them demonstrate the waveform, and most of them measuring and hold statistics of several measuring parameters ( Mean , Max, Peak to Peak, RMS etc etc).
This example is a proof that we do more today than single tasks, and when you do more, it is required more time too.
My thoughts for now these are that if some one seeks today a meter with hi speed continuity mode, he is at the same time in a risk to fall in love with a meter this not be part of our times.
Faster in response motorcycles these were ancient two stroke 500cc, and we send them to museums because 4 Stroke Engines have more over all benefits.