Lots and lots of people have tried that.... and they ended up here with a green pool. The problem is that the chlorine in those pucks goes away, but the CYA remains and builds up, requiring higher and higher levels of chlorine to remain sanitary and algae-free. Here's something I wrote a few years ago.
We'll take a 16000 gallon pool, because that's what I have. On a fresh fill, prominent national pool chain recommends 2.5 pounds pf stabilizer per 10,000 gallons, which works out nicely to 4 pounds which brings CYA to 30.
With an average loss of 2 PPM/Day or 14 ppm/week, I'll have added 8.6 PPM/CYA if I used trichlor pucks perfectly. And they recommend a weekly "shock" of dichlor between 5 and 10 FC.. 2-3 oz per 10,000 gallons. Split the difference; I'll add 4 oz. CYA went up another .9.
So..by the end of week one, I have added 9.5 more CYA. It is now 39.5. Minimum FC for that is 3, so I'm probably okay.
Week two, up to 49 CYA.
Week three, 58.5. Minimum FC should be 5, but they recommend 3 as ideal, so the pool looks a bit hazy. So I'll toss in a little extra dichlor "shock" to jack FC up to 10. Which adds another 6.4 CYA. Keeping count? We're up to 64.9 now.
That caught the algae just in time.. we had two weeks of good luck. A steady diet of pucks and 4 oz. "shock" each week only added another 19, up to 73.9 now.
Week 6 it started looking funky, so we "shocked"it once again. CYA is up to 99.3. But minimum FC to keep algae at bay is 8, and we're still holding things to 3, because prominent national chain's preprinted sheet shows that as ideal. So algae got a toehold and the pool has a bit of a tint. So we throw two whole bags of dichlor in which jacks it another 7.6. By the time week 7 is over, we're at 116.4, because we had pucks in the floater the whole time.
So...in 7 weeks, from 30 to 116.4. Let's say there are no more algae outbreaks because they sold me a huge bucket of phos-free and another of yellow-out monopersulfate "shock" Nothing but the pucks and the extra 4 oz of dichlor "shock" weekly. So the next 7 weeks added 66.5, which brings the total to 182.9 CYA.
Now if we didn't understand this and things looked a bit hazy, we might throw an extra puck or two in the floater every couple weeks, which will drive it over 200 easily.
It's a vicious cycle. You have inadequate free chlorine for the stabilizer level so you get algae, so you turn up the chlorinator to raise FC which also raises CYA which means you need more FC so you turn up the chlorinator to raise FC which also raises CYA which means you need more FC so you turn up the chlorinator to raise FC which also raises CYA which means you need more FC so you turn up the chlorinator and then all the sudden, your pool turns cloudy and green. It wasn't all the sudden. It was building for weeks.