Baseline thought: The TFP method/recommendations rely on maintaining free chlorine within a range (based on the CYA level), especially keeping it above the minimum at all times, and doing so in a way that doesn't constantly increase CYA or calcium levels (as all slow-release forms like tablets will do). Doing so keeps the pool clear and clean at all times. That's as opposed to some pool store and pool service methods that often let chlorine levels go very low (too low in our opinion), either because they aren't adding often enough or because there isn't routine testing and adjusting to always be above minimums. They compensate for this by "shocking" either on a schedule or when algae starts forming, and using algaecides and other chemicals to hide the problems.
I've chlorinated 3 ways over the last 6 years:
1) Liquid chlorine manually poured in the pool. In most cases this can't be left to once a week. I could often get away with every 2-3 days, once you get a feel for how much chlorine is lose to the sun etc each day. Typically added 1/4-1/2 gallon a day (my chlorine use varies significantly if the solar cover is on all day or not). Not too inconvenient when home and popping out to the yard anyway, but less so when working or away for a longer time.
2) Liquid chlorine injected by Stenner pump. I used a WiFi timer so I could adjust the run time after testing (i.e. if the FC level is climing day to day reduce the time, if dropping day to day add to the time). A lot more automated especially when away, but still had to go get liquid chlorine (in the middle of the summer 8 gallons every 2-3 weeks) and carry it to the back yard. Became less convenient when the pool store on my way home from work closed (and with working at home for now).
3) SWCG (I installed this summer). So far I'm loving it. Yes, there's an upfront cost, ranging from $625 (what I paid for a 40k-gal-rated generic unit) that I installed myself to $1000-1500+. Calculating the current cost of chlorine, my breakeven is ~3 years, so if this cheap unit lasts longer I'll be ahead. But more importantly, I didn't realize how nice it is to not lug chlorine home until I didn't have to do it! Replacement cells for generic SWCGs like this go for $300-$400, and higher end cells $500-$800. Definitely not thousands -- and you can replace the cells yourself, even if originally professionally installed. So once the initial investment in the control unit is covered, the payback is even quicker on replacement cells -- even $800 every 8 years is equivalent to ~25 gallons of chlorine.
There's nothing wrong with any of these options, just a personal tradeoff of lifestyle, convenience, and desire to pay now vs later.