For every 10 ppm Free Chlorine (FC) added by Trichlor, it also increases Cyanuric Acid (CYA) by 6 ppm. The CYA primarily gets reduced through dilution of the water. Those with summer or winter rains where the water overflows the pool would have the water diluted and the CYA level reduced from what it would otherwise be. Those with a sand filter that gets backwashed or a filter that is regularly cleaned would have water dilution. There is also a slow oxdiation of CYA by chlorine, though that is only around 2 ppm or so per month in most pools. There can also be a drop in CYA over the winter if the pool is "let go" and the FC goes to zero, but this process can result in ammonia which can take a lot of chlorine to get rid of (not everyone experiences this -- sometimes the CYA drops and no ammonia appears to be present).
In my own pool when I first started using Trichlor tablets 7 years ago, my CYA rose from 30 ppm to around 150 ppm in 1-1/2 swim seasons -- 10-11 months of active use (the chlorine addition over the winter was very low). The daily chlorine addition was around 0.7 ppm FC per day at that time (about one 8-ounce 3" Trichlor puck added every 5 days for 16,000 gallons). I have a mostly opaque pool cover and the pool wasn't used as much then though was kept warm (around 88ºF). I also have an oversized cartridge filter that only needs cleaning once a year. Over the winter, I had a pool cover pump that removed the winter rain water and put it into the sewer (not in the pool). So I had very little water dilution. Lo and behold, 30+10.5*30*0.7*0.6 = 162 ppm which is a little higher than the 150 ppm I measured, probably due to the small amount of water carry-out and splash overflow from the pool.
I normally tried to maintain a 3 ppm FC, but after the 1-1/2 seasons there was a mysterious (to me at the time) chlorine demand and I was having a harder time keeping up with chlorine, having to use more tablets. The water started to turn dull on the way to cloudy. It was an impending algae bloom. The only reason the water lasted as long as it did before problems started was that I was using an algaecide that had PolyQuat, but I was only using it every other week. Had I used it every week, I probably could have gone to 200 ppm CYA or perhaps higher. Had I not used any algaecide at all, I probably would have run into problems much sooner, perhaps around 60 ppm CYA or so. My fill water has around 400 ppb phosphates that got added to the pool when it was used from evaporation/refill and, of course, upon initial filling.
As for Thinkly's CYA test that always measured over 100 even after a drain/refill, that would imply that if you were to test tap water that it too would have registered over 100 ppm -- that mixing the CYA reagent with any water would turn cloudy. This is the only report like this we have ever seen. I'm not saying it's not real, but it's definitely not a common or even infrequent experience -- it is a solitary one. Thinkly, if you still have that CYA test and reagents, try testing tap water and see what you come up with. If it turns cloudy, then the reagent must be bad.
As for people using Trichlor tabs and not having problems, of course there are many pools like that, but it's a risk you are taking because there are many pools that do develop algae. Yes, if you have some water dilution and the CYA doesn't get too high, then even 3 ppm FC with 100 ppm CYA might work if you shock the pool weekly to make up for nascent algae growth that could get started and you don't have too reactive a pool in terms of algae nutrients. However, this is a risk. The pool store in my area that does service on thousands of pools keeps the FC at around 4.5 ppm and dilutes the water in any pool when the CYA gets above 100 ppm because they found that too many pools developed algae if they didn't do that (i.e. if they let the CYA keep rising to the 200 ppm the manufacturers claimed was "no problem"). This pool service did not understand the FC/CYA relationship -- this came from their own experience. Because they only visit the pools once a week, they use Trichlor tabs/pucks in either inline chlorinators or floating feeders.
Most residential pools do in fact use Trichlor pucks/tabs, but many also use additional products from the pool store including algaecides, copper ion systems, weekly shocking, etc. that can prevent algae growth at extra cost and with potential consequences (such as staining from the copper). Many pools get water diluted from winter rains and have sand filters with significant backwashing so keep the CYA level in check. And there are many pools that get dull/cloudy water or algae and go to pool stores for solutions. There are literally thousands of pool owners that have come to this and other sites with algae problems and it's growing every year as word spreads -- sure, that pales compared to the 8 million pools in the U.S., but most people with pool problems go to their pool store and not to the Internet finding this site.
Trichlor tabs/pucks are obviously more convenient than manually dosing with chlorine every day or two. So of course people can use them if they understand the consequences and risks. That is all this site is about -- education. It's your pool and you can do what you want with it, but the FC/CYA relationship is real and the risk for developing algae in high CYA pools is real and seen over and over and over and over again when people come to this forum (and others) initially with algae or dull/cloudy pools or early stages with high chlorine demand. Not everyone will experience this, but for those who do there is a simple solution and that's all that is taught.
Richard