It is not a certainty that a pool high in CYA will get algae because it also depends on whether there are sufficient algae nutrients in the pool water. Also, people with smaller pools and sand filters get more water dilution from backwashing and some areas have summer rains that overflow the pool to dilute the water and some people have short swim seasons and lose some or all of their CYA over the winter. Also, some people use algaecides or phosphate removers that let one get away with higher CYA levels. Also, many people shock their pools weekly which helps make up for too low an FC/CYA ratio during the week.
In my own pool years ago, I used Trichlor pucks in a floating feeder with a 3 ppm FC target and used algaecide every other week. I had no problem the first year, but I had a mostly opaque pool cover so had low chlorine usage of 0.7 ppm FC per day and a 7-month swim season. I didn't have any summer rains and I had a pool cover pump that put any winter rains into the sewer and I had an oversized cartridge filter that only needed cleaning once a year. So I had very little water dilution. Halfway during the second season, I had trouble maintaining the chlorine level and used more pucks to compensate, but the water still started to turn dull and then cloudy -- an impending algae bloom. Though I started out with 30 ppm CYA, I had 150 ppm CYA after 10-11 months of swim seasons -- 30 + 0.7*30*10.5*0.61 = 165 ppm (so there was some loss from splash-out/carry-out/oxidation of CYA).
As for pool stores selling Trichlor, they also have many pool owners come in with algae problems and are also sold algaecides, phosphate removers, clarifiers, flocculants at much higher profit margins (especially for the manufacturers) than the chlorine. This is what makes it a multi-billion dollar business. A large number of people coming to this forum have algae problems and the vast majority of them are due to high CYA from continued use of stabilized chlorine products.
So you may very well not have any problems just using Trichlor, but remember what Clint Eastwood said in Dirty Harry -- "you’ve got to ask yourself one question: 'Do I feel lucky?'" You could certainly try using Trichlor and see how your CYA goes over time. Maybe you've got enough dilution to keep it in check or can increase the FC as it climbs. The key is that you'll know enough to test for it and know how to deal with any problems if they occur.