if the whole industry is wrong selling everyone what it has been selling, why? I mean, it has to work somehow, but there is probably ways...like using nonstabilized shock? if there is no way of removing excess cyanuric, and it will accumulate, and absolute majority of peope uses stabilized tablets, how has it been working so far?
The short answer is that it doesn't work, for a lot of people, probably around 20% of pools in any given season (that's over 1-1/2 million pools with problems each year). However, some pools are naturally low in critical algae nutrients (phosphates and nitrates) so that even when the CYA gets high and the FC isn't raised proportionately they don't get algae. Also, some pools are in areas with shorter swim seasons, summer rain overflow, winter rain dilution (closing), sand filters with backwashing, and other water dilution that keeps the CYA level in check season to season.
However, it is a chemical fact that for every 10 ppm Free Chlorine (FC) added by Trichlor, it will also increase Cyanuric Acid (CYA) by 6 ppm. So when some pools run into problems and their pool owners go to the pool store, the store has lots of "solutions" such as algaecides, phosphate removers, clarifiers, flocculants, "shock" products, enzymes, etc. Even a single category such as algaecides has several choices including products you add every week (linear and Polyquat) or those you mostly add once (copper ions), but they have downsides in addition to their extra cost where copper, for example, can stain plaster surfaces and turn blond hair greenish while linear quats can foam and have a higher chlorine demand. The phosphate removers don't have that kind of side effect but they can be costly (especially for the initial dose) if phosphate levels are high.
So there is more than one way to manage a pool. The way to do so using the minimal amount of these extra products is to primarily use chlorinating liquid or bleach for chlorine because it doesn't add calcium (which Cal-Hypo does) nor CYA (which Trichlor and Dichlor do). However, you are correct that it is less convenient in some ways in that it is more weight to carry (12.5% chlorinating liquid is 7 times heavier than Trichlor and 8.25% bleach is nearly 11 times heavier than Trichlor -- but they aren't more expensive overall) and you need to add it every day or two unless you have a pool cover in which case if it is relatively opaque you could add chlorine twice a week. For more convenience, some people get automatic dosing systems such as peristaltic pumps or The Liquidator or they get a saltwater chlorine generator.
You can operate your pool with Trichlor pucks if you either keep the CYA level in check with water dilution or you use supplemental products (at extra cost) to prevent algae (unless your pool is already low in algae nutrients) or you proportionally raise the FC level as the CYA level gets higher or some combination of these techniques, but this forum is mostly about avoiding the use of Trichlor and its CYA buildup so using it for vacation or when you need the CYA to be higher (slowly -- if needed more quickly, then one uses pure CYA instead).
Some pool services are acutely aware of these issues and deal with them in a variety of different ways. In my area, a company that services around 2000 pools targets 4.5 ppm FC and drain water when the CYA gets over 100 ppm, but some pools still get algae (because 4.5 ppm FC is not enough to prevent algae when the CYA is higher) in which case they first try shocking and if the algae still comes back then they use a phosphate remover. Other pool services use algaecides regularly or use copper (and do their best to prevent staining by keeping pH lower). Some other pool services use chlorinating liquid or chlorine gas or a combination and raise the FC high and have a higher CYA so that the FC lasts through the week (i.e. the FC swings a lot). It's harder for them than pool owners because they aren't there every day to take care of the pool.
With so many pools going bad each year, this is why so many people get fed up with the pool stores and scour the Internet for solutions and run into this site. There are more than 400,000 people per month visiting Trouble Free Pool during the peak summer season and over 88,000 have become members with about half posting (in other words, most people are "lurkers"). What is taught here is to get a good test kit so that you can get proper test results and then to manage your pool the way you want armed with knowledge of what each chemical does in your pool. If you choose to stick with Trichlor, that's your choice, but at least you won't be surprised when the CYA climbs and what that means. It's your pool and you can and should manage it the way that works best for you. Knowledge is power and this site is about telling you the truth. What you do with it is up to you.