IMO not doing a water change might disrupt the cycle due to excessive pH swings and excess nitrite poisoning the very bacteria that are feeding it. Or have we indeed found that the filter bacteria live in the water after all? In a sense you may have to start again as you will have to add new ammonia, but your filter media and tank surfaces have retained the beneficial bacteria, so you won't have lost any days of the cycling process. Whether you change water or not will surely depend on what your test results are showing you.
Beneficial bacteria does not live in the water column as far as I know, mainly because these bacteria needs to attach to any surfaces in the aquarium, including plants, substrate and decor etc and the bacteria thus then produces a bio-film that protects them.
A very knowledgeable and respected former member of this forum, TwoTankAmin, wrote the cycling article and states - "In a cycled tank the nitrifying bacteria does not live free floating in the water"
If you give the bacteria all they need, they will multiply. Even more importantly, they will produce a bio-film which they use to attach themselves to surfaces in your filter and all over your tank and which protects them. In a cycled tank the nitrifying bacteria do not live free floating in the water.
Quoted from the Fishless cycling article -
https://www.fishforums.net/threads/cycling-your-new-fresh-water-tank-read-this-first.421488/
The only times one should change tank water during the fishless cycling process is when one runs into difficulty such as mistakenly adding too much ammonia or perhaps if the pH changes drastically, then partly changing the water will reduce ammonia levels or increases pH back to desired levels and yes indeed, Myraan is correct in this won't disrupt the cycling process too much because as you say, most of the beneficial bacteria will already have be retained having been formed on surfaces including in the filter.
In worst case scenarios is when the cycle has stalled or crashed, then the answer is the to restart the whole cycle again is by doing as close to 100% water change as possible.
Not doing a water change should not disrupt the cycling process nor excessive pH levels swings as long as there is sufficient water surface agitation for oxygen exchange and water temperature at optimum levels of 24-29C (75-85F).
Large pH level changes can be down to a number of factors such as having crushed coral in substrate, certain peat/wood decor can reduce pH levels, even adding certain chemicals that alters pH/kH levels.
But most keepers will find that pH naturally drops in small increments over time but not so much of a drop over 6 weeks or so of the average cycling process timescale that it causes concern to change the tank water usually.
There are exceptions of course, but generally speaking most aquarist should not have to change tank water during the fishless cycling process.